MATHS & REASONING BY - DR.V.K.OMAR
कैलेंडर
ईसा पूर्व , (B.C.) BEFORE THE BIRTH OF JESUS CHRIST
ईसा बाद (A.D.) ANNO DOMINI or IN THE YEAR OF LARD
विश्व में लगभग 75 कैलेण्डर प्रचलित हैं।
सर्वाधिक प्रचलित कैलेण्डर ग्रिगेरिअन कैलेण्डर है।
ग्रेगेरिएन कैलेण्डर को रोम के तेहरवे पॉप ग्रेगरी ने २४ फरवरी 1582 को लागु किया यह 15 अक्टूबर 1582 से शुरू हुआ।
बुद्ध सम्वत - श्री लंका की गणना के अनुसार 544 ईसा पूर्व स्थापित।
महावीर सम्वत - महावीर जैन द्वारा 527 ईसा पूर्व।
विक्रम सम्वत या मालवा सम्वत या कृत सम्वत - 57 ईसा पूर्व मालवा के शासक विक्रमादित्य द्वारा (शकों को पराजित करने की ख़ुशी में )
शक सम्वत - ७८ ईसा पूर्व कुषाण शासक कनिष्क ।
कलचुरि - चेदि सम्वत - 248 ईसवी अमीर शासक ईश्वर सेन ।
गुप्त सम्वत या बल्लमी सम्वत - 319 ईसवी में चन्द्रगुप्त प्रथम द्वारा स्थापित ।
हर्ष सम्वत - 606 ईसवी में वर्धन शासक हर्ष वर्धन द्वारा स्थापित ।
कोलम सम्वत - 825 ईसवी में कल्याणी के चालुक्य शासक विक्रमादित्य चतुर्थ।
इलाही सम्वत - 1583 ईसवी में मुग़ल शासक अकबर द्वारा।
नानक शाही सम्वत - श्री बंदा सिंह बहादुर द्वारा 1710 ईसवी मेँ अपनाया गया। आरम्भ सिख गुरु श्री नानक देव जी के जन्म वर्ष ( १५ अप्रैल १४६९)माना गया।
देश आजाद के बाद नवम्बर १९५२ मेँ वैज्ञानिक और औद्योगिक परिषद् द्वारा पंचांग सुधार समिति का गठन किया गया।
इस समिति ने 1955 मेँ अपनी रिपोर्ट मेँ विक्रम सम्वत को भी स्वीकार करने की सिफारिश की।
तत्कालीन प्रधानमंत्री पंडित जवाहर लाल नेहरू के आग्रह पर ग्रिगेरियन कैलेण्डर को सरकारी कामकाज हेतु 22 मार्च 1957 को स्वीकार किया गया।
पंचांग के १२ महीने -
चैत्र , बैशाख , ज्येष्ठ , आषाढ़ , श्रावण , भाद्रपद,आश्विन,कार्तिक,आग्रहन,पौष,माघ,फाल्गुन।
राष्ट्रीय पंचांग का प्रारम्भ चैत्र प्रथमा तिथि को होता है।
सामान्य वर्ष में चैत्र प्रथमा तिथि 22 मार्च , लीप वर्ष में 21 मार्च को प्रारम्भ होता है।
कैलेण्डर की 5 इकाई होती हैं - दिन,तिथि,सप्ताह,माह वर्ष।
एक दिन मेँ 23 घंटा 56 मिनट 4.09 सेकंड होते हैं। यह अवधि पृथ्वी द्वारा अपनी धुरी पर एक चक्कर लगाने में लिया गया समय है।
1 सौर वर्ष में 365 दिन 5 घंटा 48 मिनट 45.51 सेकण्ड अर्थात 365.2422 दिन होते हैं।
after Christ (A.D.) ANNO DOMINI or IN THE YEAR OF LARD
Kolam Samvat - Vikramaditya IV, the Chalukya ruler of Kalyani in 825 AD.
Ilahi Samvat - by the Mughal Emperor Akbar in 1583 AD.
Nanak Shahi Samvat - Adopted by Shri Banda Singh Bahadur in 1710 AD. The beginning was considered to be the birth year of Sikh Guru Shri Nanak Dev Ji (15 April 1469).
After the independence of the country, in November 1952, the Panchang Reform Committee was formed by the Scientific and Industrial Council.
This committee in its report in 1955 recommended the acceptance of Vikram Samvat as well.
On the request of the then Prime Minister Pandit Jawaharlal Nehru, the Gregorian calendar was accepted for official work on 22 March 1957.
12 Months of Panchang -
Chaitra, Baishakh, Jyeshtha, Ashadha, Shravan, Bhadrapada, Ashwin, Kartik, Agrahan, Paush, Magha, Phalgun.
The National Panchang begins on Chaitra Pratham Tithi.
March 22 in a normal year begins on March 21 in a leap year.
Calendar has 5 units - day, date, week, month and year.
There are 23 hours 56 minutes 4.09 seconds in a day. This period is the time taken by the earth to make one revolution on its axis.
There are 365 days 5 hours 48 minutes 45.51 seconds i.e. 365.2422 days in 1 solar year.
There are 365 days i.e. one odd day in an ordinary year. Leap year has 366 days i.e. 2 odd days.
There are 76 ordinary years + 24 leap years in 100 years i.e. 5 odd days.
There are 3 odd days in 200 years.
There is 1 odd day in 300 years.
There are 0 odd days in 400 years.
The first day of a centenary year can be Monday, Tuesday, Thursday, Friday, Saturday.
The last day of a centenary year cannot be Tuesday, Thursday, Saturday but Wednesday, Friday, Sunday.
The first and last day of an ordinary year are the same.
कैलेंडर का अविष्कार रोम के तेरहवें पॉप ने किया था पोप ग्रेगरी ने क्राइस्ट की जन्म तिथि 1 जनवरी सन एक निश्चित करते हुए उसी दिन से अपने कैलेंडर को शुरू किया 1752 में पूरे ब्रिटिश साम्राज्य में इसका प्रयोग प्रारंभ हुआ और तब से लेकर इसकी महत्ता बढ़ती गई अपनी वैज्ञानिक संकल्पना के कारण ग्रेगोरियन कैलेंडर अंतरराष्ट्रीय कैलेंडर के रूप में प्रसिद्ध हो गया इसीलिए इसको ग्रेगोरियन कैलेंडर के नाम से भी जाना जाता है।
कैलेंडर की पांच प्रमुख इकाई होती हैं जो निम्न प्रकार हैं: कैलेंडर की इकाई- दिन, सप्ताह, तिथि, माह, वर्ष
दिन - सप्ताह के सातवें भाग को 1 दिन का जाता है। इन्हें अलग-अलग 7 ग्रहों के नाम के द्वारा निरूपित किया जाता है जैसे- रविवार, सोमवार, मंगलवार, बुधवार, बृहस्पतिवार, शुक्रवार और शनिवार
सप्ताह - किसी महीने के चौथे या वर्ष के 48वे भाग को सप्ताह कहा जाता है 1 सप्ताह में कुल 7 दिन होते हैं जिनमें पहला दिन रविवार और अंतिम दिन शनिवार होता है।
तिथि- किसी महीने में 1 से 28/29/30 /31 तक के अंको द्वारा निरूपित अवधि को तिथि कहा जाता है।
माह - वर्ष के बारहवे भाग को माह कहते हैं 1 वर्ष के अंतर्गत जनवरी, फरवरी, मार्च, अप्रैल, मई, जून, जुलाई, अगस्त, सितंबर, अक्टूबर, नवंबर, दिसंबरवर्ष महीने होते हैं। जिनमें से 7 महीने जनवरी, मार्च, मई, जुलाई, अगस्त, अक्टूबर एवं दिसंबर को 31 तथा 4 महीने अप्रैल, जून, सितंबर, नवंबर को 30 एवं शेष 1 महीना अर्थात फरवरी को 28 या 29 तिथियों के द्वारा निरूपित किया जाता है.
सामान्य वर्ष मेँ फरवरी को 28 दिन और अगर लीप वर्ष है तो 29 दिन के द्वारा निरूपित किया जाता है.
वर्ष - शताब्दी के सौवे भाग को या 12 महीने की संयुक्त अवधि को वर्ष कहते हैं सामान्य रूप से वर्ष दो प्रकार के होते हैं। सामान्य वर्ष एवं लीप वर्ष
सामान्य वर्ष - जो 4 से पूर्णतया विभक्त नहीं होते हैं ऐसे शताब्दी वर्ष जो 400 से पूर्णतया विभाजित नहीं होते हैं ऐसे वर्ष को सामान्य वर्ष कहते हैं किसी भी सामान्य वर्ष में कुल 365 दिन होते हैं . जैसे- 1987, 1989, 1990, 1991 एवं 1800 यहां पर ध्यान देने वाली बात है कि अट्ठारह सौ एक शताब्दी वर्ष है लेकिन इसमें 400 से भाग नहीं जा रहा है इसलिए यह सामान्य वर्ष है.
लीप वर्ष - ऐसे वर्ष जो 4 से पूर्णतया विभक्त हैं अथवा ऐसे शताब्दी वर्ष जो 400 से पूर्णतया विभाजित हो जाते हैं लीप वर्ष कहलाते हैं. जैसे- सन 1984, 1988, 1992, 1996 एवं सन 2000 लीप वर्ष ध्यान देने योग्य बात है कि सन 2000 शताब्दी वर्ष है लेकिन यह 400 से पूर्णतया विभाजित है आता है लीप वर्ष है.
उपर्युक्त तथ्यों से अवगत होने के बाद अब हम वर्ष, सप्ताह दिन एवं अल्ट्रा मॉडर्न यूनिक् ट्रिक के उन तथ्यों पर एक नजर डालते हैं जो कैलेंडर से संबंधित प्रश्नों को हल करने के लिए अत्यंत आवश्यक होते हैं -
सामान्य वर्ष- सामान्य वर्ष में पहला और अंतिम दिन दोनों ही दिन समान होते हैं जैसे यदि 1 जनवरी को सोमवार है तो निश्चित रूप से 31 दिसंबर को भी सोमवार होगा।
लीप वर्ष- लीप वर्ष में वर्ष का पहला और अंतिम दिन दोनों ही भिन्न भिन्न होते हैं पहला दिन की तुलना में अंतिम दिन 1 दिन आगे बढ़ जाता है मान लेते हैं 1 जनवरी को सोमवार है तो 31 दिसंबर को लीप वर्ष होने पर मंगलवार होगा।
सप्ताह- प्रत्येक सप्ताह में कुल 7 दिन होते हैं.
दिन- किसी भी दिन में 7 दिन जोड़ने अथवा घटाने पर पुनः वही दिन प्राप्त हो जाता है जैसे यदि 1 जनवरी को सोमवार है तो 7 जोड़ने से 8 जनवरी को भी सोमवार होगा।
सामान्य वर्ष - सामान्य वर्ष में किसी निश्चित तिथि पर व्यवस्थित दिन अगले वर्ष अपने वर्ष की तुलना में 1 दिन बढ़ जाता है. जैसे- यदि 1 जनवरी 2021 को सोमवार है तो 1 जनवरी 2002 को मंगलवार होगा और 1 जनवरी 2003 को बुधवार होगा।
लीप वर्ष- लीप वर्ष में किसी निश्चित तिथि पर व्यवस्थित दिन अगले वर्ष अपने पिछले सामान्य वर्ष की तुलना में 2 दिन आगे बढ़ जाता है. जैसे- हम मान लेते हैं कि 4 जून सन 1983 को शनिवार है तो 4 जून 1984 को 2 दिन आगे अर्थात सोमवार होगा।
कांसेप्ट ऑफ़ - के बाद, के पहले, से बाद, से पहले वाले प्रश्नों में इनका प्रयोग करते हैं -
के बाद - मान लेते हैं कोई क्वेश्चन है 10 फरवरी के 5 दिन बाद की तिथि बताइए यहां पर 10 फरवरी के बाद की छठवीं तिथि अर्थात 16 तारीख के बारे में बात हो रही है.
के पहले,से पहले (उतना ही घटायें)
10 अगस्त से 5 दिन पहले = 10 - 5 = 5
सोमवार से 2 दिन पहले = सोमवार - 2 = शनिवार
10 अगस्त के 5 दिन पहले = 10 - 5 = 5
सोमवार के 2 दिन पहले = सोमवार - 2 = शनिवार
बृहस्पतिवार के 2 दिन बाद का दिन बृहस्पति के बाद का तीसरा दिन यानी कि रविवार की बात हो रही है
से बाद (उतना ही बढ़ाकर)
१० अगस्त से ५ दिन बाद = 10 + 5 = 15
सोमवार से २ दिन बाद = सोमवार + 2 = बुधवार
अब हम बात करते हैं विषम दिनों के बारे में यह किसी भी दी गई तारीख को दिन ज्ञात करना है तो उसमें भी विषम दिन की अत्यंत महत्त्वपूर्ण भूमिका होती है.
रविवार 0 विषम दिन , सोमवार 1 विषम दिन, मंगलवार दो विषम दिन, बुधवार 3 विषम दिन, बृहस्पतिवार 4 विषम दिन दिन, शुक्रवार 5 विषम दिन और शनिवार 6 विषम दिन माना गया है
The calendar was invented by the thirteenth pope of Rome. Pope Gregory started his calendar from the same day by fixing the date of birth of Christ on 1 January, it was used throughout the British Empire in 1752 and since then its importance has increased Due to its scientific concept, the Gregorian calendar became famous as the international calendar, hence it is also known as the Gregorian calendar.
There are five major units of calendar which are as follows: Unit of calendar- day, week, date, month, year
Day - The seventh part of the week is marked by 1 day. They are denoted by the names of 7 different planets such as- Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday.
Week - The fourth part of a month or the 48th part of the year is called a week. There are total 7 days in 1 week in which the first day is Sunday and the last day is Saturday.
Date- The period in a month represented by the numbers from 1 to 28/29/30/31 is called date.
Month - The twelfth part of the year is called month, under 1 year there are months of January, February, March, April, May, June, July, August, September, October, November, December. Out of which 7 months January, March, May, July, August, October and December are represented by 31 and 4 months April, June, September, November by 30 and the remaining 1 month i.e. February by 28 or 29 dates.
February is represented by 28 days in a normal year and 29 days if it is a leap year.
Year - The hundredth part of a century or the combined period of 12 months is called a year, in general there are two types of years. normal year and leap year
Ordinary Years - Centenary years that are not completely divisible by 4, such years are called ordinary years, in any ordinary year there are total 365 days. For example, 1987, 1989, 1990, 1991 and 1800, it is to be noted that eighteen hundred is a century year but it is not divided by 400, so it is a normal year.
Leap Years - Years which are completely divisible by 4 or centenary years which are completely divisible by 400 are called leap years. For example, the years 1984, 1988, 1992, 1996 and 2000 are leap years. It is worth noting that the year 2000 is a centenary year but it is completely divisible by 400. It is a leap year.
After being aware of the above facts, now let us have a look at those facts of year, week day and ultra modern unique trick which are very important to solve the questions related to calendar -
Ordinary Year- In a normal year both the first and last day are the same e.g. if 1st January is Monday then surely 31st December will also be Monday.
Leap year - In leap year, both the first and last day of the year are different, the last day is moved forward by 1 day as compared to the first day. Let's say January 1 is Monday, then December 31 will be Tuesday if it is a leap year.
Week- There are total 7 days in each week.
Day- Adding or subtracting 7 days in any day again gives the same day as if 1st of January is Monday, then adding 7 to 8th January will also be Monday.
Normal Year - In a normal year the arranged day on a certain date is increased by 1 day in the next year as compared to its year. For example, if 1st January 2021 is Monday, then 1st January 2002 will be Tuesday and 1st January 2003 will be Wednesday.
Leap Year - In a leap year, the day arranged on a certain date moves forward by 2 days to the next year as compared to its previous normal year. For example, if we assume that 4th June 1983 is Saturday, then 4th June 1984 will be 2 days ahead i.e. Monday.
Concept of - After, before, after, before, we use these in questions like -
After - Let's say there is a question, tell the date after 5 days after 10th February, here we are talking about the 6th date after 10th February i.e. 16th.
before, before (subtract as much)
5 days before 10th August = 10 - 5 = 5
2 days before Monday = Monday - 2 = Saturday
5 days before 10th August = 10 - 5 = 5
2 days before Monday = Monday - 2 = Saturday
2 days after thursday The third day after thursday i.e. Sunday is being talked about.
after (increasing as much)
5 days after 10th August = 10 + 5 = 15
2 days after Monday = Monday + 2 = Wednesday
Now we talk about odd days, if it is to find the day on any given date, then odd day has a very important role in that too.
Sunday has 0 odd days, Monday 1 odd day, Tuesday 2 odd days, Wednesday 3 odd days, Thursday 4 odd days, Friday 5 odd days and Saturday 6 odd days
(1) Karan remembers that his sister's birthday is not after 18th
August. Karan's mother remembers that Karan's sister birthday is
before 20th August but after 17th August. On which date of
August is Karan's sister birthday?
करन को याद है की उसकी बहन का जन्मददन 18 अगस्त के बाद नहीीं है।
करन की मााँ को याद है दक करन की बहन का जन्मददन 20 अगस्त से पहले
लेदकन 17 अगस्त के बाद है। करन की बहन का जन्मददन अगस्त की दकस
तारीख को है?
SSCCGL201710AUG-S1 : 11
(a) 18 (b) 17 (c) 19 (d) 20
(2) Advik's birthday is on Monday 19th June. On what day of the
week will be Nishith's Birthday in the same year if Nishith was
born on 17th November?
अदिक का जन्मददन सोमवार 19 जून को है। यदद दनशीथ का जन्म 17 November को है तो उसी वर्ष दनशीथ का जन्मददन सप्ताह में दकस ददन होगा?
SSCCGL201721AUG-S3 : 10
(a) Saturday/शदनवार (b) Wednesday/बुधवार
week will be Pinky's Birthday in the same year if Pinky was born
on 22nd September?
बॉबी का जन्मददन 5 जून सोमवार को है। उसी वर्ष दपींकी का जन्मददन सप्ताह
के दकस ददन को आएगा यदद दपींकी का जन्म 22 दसतींबर को हुआ है?
(3) Bobby's birthday is on Monday 5th June. On what day of the
SSCCGL201722AUG-S2 : 10
(a) Saturdayशदनवार (b) Wednesdayबुधवार
(c) Fridayशुक्रवार (d) Sundayरदववार
(4) Hansh's birthday is on Monday 5th June. On what day of the
week will be Tushar's Birthday in the same year if Tushar was
born on 11th December?
हींश का जन्मददन सोमवार 5 जून को है। यदद तुर्ार का जन्म 11 ददसींबर को
हुआ था तो उसी वर्ष तुर्ार का जन्मददन सप्ताह में दकस ददन होगा?
SSCCGL201717AUG-S1 : 10
(a) Sunday / रदववार (b) Wednesday / बुधवार
(c) Monday / सोमवार (d) Tuesday / मींगलवार
(5) Akshar remembers that the match is after 26th April but
before 30th April, while Suresh remembers that the match is
after 22nd April but before 28th April. On which date of April is
the match?
अक्षर को याद है की मैच 26 अप्रैल के बाद लेदकन 30 अप्रैल से पहले है,
जबकी सुरेश को याद है की मैच 22 अप्रैल के बाद लेदकन 28 अप्रैल से पहले
है। मैच अप्रैल की दकस तारीख को है?
SSCCGL201711AUG-S2 : 10
(a) 29 (b) 26 (c) 27 (d) 28
(6) Divit's birthday is on Friday 30th June. On what day of the
week will be Samar's Birthday in the same year if Samar was born
on 15th November?
दददवत का जन् मददन शुक्रवार 30 जून को है। यदद समर का जन् म15 नबींबर को
हुआ था तो उसी वर्ष समर का जन् मददन सप् ताह में दकस ददन होगा?
SSCCGL201717AUG-S2 : 10
(a) Tuesday / मींगलवार (b) Friday / शुक्रवार
(c) Wednesday / बुधवार (d) Saturday / शदनवार
(7) Chirag's birthday is on Thursday 1st June. On what day of the
week will be Reyansh's Birthday in the same year if Reyansh was
born on 3rd December?
दचराग का जन् मददन गुरूवार 1 जून को है। यदद ररयाींश का जन् म 3 ददसम् बर
को हुआ था तो उसी वर्ष ररयाींश का जन् मददन सप् ताह में दकस ददन होगा?
SSCCGL201717AUG-S3 : 10
(a) Wednesday / बुधवार (b) Sunday / रदववार
(c) Friday / शुक्रवार (d) Saturday / शदनवार
(8) Eshan's birthday is on Friday 10th March. On what day of the
week will be Shlok's Birthday in the same year if Shlok was born
फै याज का जन्मददन बुधवार 12 अप्रैल को है| यदद श्रेय का जन्म 2 अक्टू बर
को हुआ था तो उसी वर्ष श्रेय का जन्मददन सप्ताह में दकस ददन होगा?
SSCCGL201718AUG-S2 : 10
(a) Monday / सोमवार (b) Wednesday / बुधवार
(c) Friday / शुक्रवार (d) Thursday / गुरुवार
(9) Devansh\'s birthday is on Friday 14th April. On what day of
the week will be Rohan\'s Birthday in the same year if Rohan was
born on 20th September?
देवाींश का जन्मददन शुक्रवार 14 अप्रैल को है| यदद रोहन का जन्म 20 दसतींबर
को हुआ था तो उसी वर्ष रोहन का जन्मददन सप्ताह में दकस ददन होगा?
SSCCGL201718AUG-S3 : 10
(a) Tuesday / मींगलवार (b) Friday / शुक्रवार
(c) Thursday / गुरुवार (d) Wednesday / बुधवार
(10) Gurkiran's birthday is on Sunday 21st May. On what day of
the week will be Shreyas's Birthday in the same year if Shreyas
was born on 14th November?
गुरकीरण का जन्मददन रदववार 21 मई को है | यदद श्रेयास का जन्म 14 नवींबर
हुआ था तो उसी वर्ष श्रेयास का जन्मददन सप्ताह के दकस ददन होगा ?
SSCCGL201718AUG-S1 : 10
(a) Tuesday / मींगलवार (b) Wednesday / बुधवार
(c) Friday / शुक्रवार (d) Saturday / शदनवार
(11) Faiyaz's birthday is on Wednesday 12th April. On what day
of the week will be Shray's Birthday in the same year if Shray was
born on 2nd October?
फै याज का जन्मददन बुधवार 12 अप्रैल को है| यदद श्रेय का जन्म 2 अक्टू बर
को हुआ था तो उसी वर्ष श्रेय का जन्मददन सप्ताह में दकस ददन होगा?
SSCCGL201719AUG-S1 : 10
(a) Monday / सोमवार (b) Saturday / शदनवार
(c) Wednesday / बुधवार (d) Sunday / रदववार
(12) Sumitra remembers that her mother's birthday is after 13th
February but before 16th February but her brother remembers
that his mother's birthday is after 14th February but before 17th
February. On which date Sumitra's mother's birthday will be
celebrated?
सुदमत्रा को याद है दक उनकी माता का जन्न् मन 13 फरवरी के बाद लेदकन 16
फरवरी से पहले आता है लेदकन उसके भाई को याद है दक उनकी माता का
जन् मददन 14 फरवरी के बाद लेदकन 17 फरवरी से पहले आता है दकस ताररख
को सुदमत्रा की माता का जन् मददन मनाया जाएगा?
SSCCGL201716AUG-S1 : 10
(a) 13th February / 13 फरवरी (b) 14th February / 14 फरवरी
(c) 15th February / 15 फरवरी (d) 17th February / 17 फरवरी
(13) Divyansh\'s birthday is on Sunday 16th July. On what day of
the week will be Shaan\'s Birthday in the same year if Shaan was
born on 1st August?
ददव्ाींश का जन्मददन रदववार 16 जुलाई को है| यदद शान का जन्म 1 अगस्त
को हुआ था तो उसी वर्ष शान का जन्मददन सप्ताह में दकस ददन होगा?
SSCCGL201719AUG-S2 : 10
(a) Tuesday / मींगलवार (b) Monday / सोमवार
(c) Wednesday / बुधवार (d) Wednesday / बुधवार
(14) Dhruv's birthday is on Sunday 28th May. On what day of the
week will be Sahil's Birthday in the same year if Sahil was born
on 19th October?
ध्रुव का जन्मददन रदववार 28 मई को है| यदद सादहल का जन्म 19 अक्टू बर को
को हुआ था तो उसी वर्ष सादहल का जन्मददन सप्ताह में दकस ददन होगा ?
SSCCGL201719AUG-S3 : 10
(a) Saturday / शदनवार (b) Wednesday / बुधवार
(c) Thursday / गुरुवार (d) Sunday / रदववार
(15) Bhavin's birthday is on Monday 29th May. On what day of
the week will be Rachit's Birthday in the same year if Rachit was
born on 17th November?
भादवन का जन्मददन सोमवार 19 मई को है| यदद रदचत का जन्म 17 नवम्बर
को आता है तो समान वर्ष में रदचत का जन्मददन के दकस दी होगा?
SSCCGL201720AUG-S1 : 10
(a) Saturday शदनवार (b) Wednesday बुधवार
(c) Sunday रदववार (d) Friday शुक्रवार
(16) Meetu's birthday is on Wednesday 8th March. On what day
of the week will be Ritu's Birthday in the same year if Ritu was
born on 10th July?
मीतू का जन्मददन 8 माचष बुधवार को है | उसी वर्ष ऋतु का जन्मददन सप्ताह
के दकस ददन को आएगा यदद ऋतु का जन्म 10 जुलाई को हुआ है?
SSCCGL201721AUG-S1 : 10
(a) Monday / सोमवार (b) Wednesday / बुधवार
(c) Friday / शुक्रवार (d) Saturday / शदनवार
(17) Akarsh\'s birthday is on Saturday 29th July. On what day of
the week will be Ojas's Birthday in the same year if Ojas was
born on 12thAugust?
आकर्ष का जन्मददन शदनवार 29 जुलाई को है| यदद जोजस का जन्म 12
अगस्त को हुआ था तो उसी वर्ष ओजस का जन्मददन सप्ताह में दकस ददन
होगा?
SSCCGL201721AUG-S2 : 10
(a) Wednesday बुधवार (b) Friday शुक्रवार
(c) Saturday शदनवार (d) Sunday रदववार
(18) Mishti's birthday is on Thursday 27th April. On what day of
the week will be Aradhya's Birthday in the same year, if Aradhya
was born on 20th October?
दमष् टी का जन् मददन 27 अप्रेल, ददन गुरूवार को है यदद अराध् या का जन् म 20
अक् टूबर को हुआ था, तो उसी वर्षआराध् या का जन् मददन सप् ताह के दकस ददन
होगा?
SSCCGL201706AUG-S1 : 10
(a) Friday शुक्रवार (b) Wednesday बुधवार
(c) Saturday दशनवार (d)Thursday गुरुवार
SSC CGL 2017: Reasoning (Clock and Calender)
(19) Aarush\'s birthday is on Thursday 27th April. On what day of
the week will be Mitul\'s Birthday in the same year if Mitul was
born on 28th September?
आरुस का जन्मददन गुरुवार 27 अप्रैल को है। यदद दमतुल का जन्म 28
दसतींबर को हुआ था तो उसी वर्ष दमतुल का जन्मददन सप्ताह में दकस ददन
होगा?
SSCCGL201723AUG-S3 : 10
(a) Monday सोमवार (b) Thursday गुरुवार
(c) Wednesday बुधवार (d) Tuesday मींगलवार
(20) Aarav's birthday is on Sunday, 12th March . On what day of
the week will be Madhup's Birthday in the same year if Madhup
was born on 10th August?
आरव का जन्मददन रदववार 12 माचष को है| यदद मधुप 10 अगस्त को हुआ था
तो उसी वर्ष मधुप का जन्मददन सप्ताह में दकस ददन होगा ?
SSCCGL201720AUG-S2 : 10
(a) Thursday / गुरुवार (b) Wednesday / बुधवार
(c) Friday / शुक्रवार (d) Saturday / शदनवार
(21) Aayush's birthday is on Monday 22nd May. On what day of
the week will be Neerav\'s Birthday in the same year if Neerav
was born on 30th October?
आयूर् का जन्मददन सोमवार 22 मई को है। यदद नीरव का जन्म 30 अक्टू बर
को हुआ था तो उसी वर्ष नीरव का जन्मददन सप्ताह में दकस ददन होगा?
SSCCGL201722AUG-S3 : 10
(a) Monday / सोमवार (b) Wednesday / बधुवार
(c) Friday / शुक्रवार (d) Thursday / गुरुवार
(22) Nasir\'s birthday is on Thursday 18th May. On what day of
the week will be Rehan\'s Birthday in the same year if Rehan was
born on 19th August?
नादसर का जन्मददन 18 मई गुरुवार को है | उसी वर्ष रेहान का जन्मददन
सप्ताह के दकस ददन को आएगा यदद रेहान का जन्म 19 अगस्त को हुआ है ?
SSCCGL201723AUG-S1 : 10
(a) Wednesday / बधुवार (b) Saturday / शदनवार
(c) Friday / शुक्रवार (d) Thursday / गुरुवार
(23) Priya's birthday is on Tuesday 11th April. On what day of the
week will be Rani's Birthday in the same year if Rani was born on
31st August?
दप्रया का जन्मददन 11 अप्रैल मींगलवार को है | उसी वर्ष रानी का जन्मददन
सप्ताह के दकस ददन आएगा यदद रानी का जनम 31 अगस्त को हुआ है |
SSCCGL201722AUG-S1 : 10
(a) Monda y / सोमवार (b) Wednesday / बुधवार
(c) Tuesday / मींगलवार (d) Thursday / गुरुवार
(24) Aniruddh's birthday is on Sunday 2nd April. On what day of
the week will be Priyansh's Birthday in the same year if Priyansh
was born on 28th October?
अदनरुद्ध का जन्मददन ररववार 2 अप्रैल को है। यदद दप्रयाींश का जन्म 28
अक्टू बर को हुआ था तो उसी वर्ष दप्रयाींश का जन्मददन सप्ताह में दकस ददन
होगा?
SSCCGL201723AUG-S2 : 10
(a) Saturday दशनवार (b) Wednesday बुधवार
(c) Friday शुक्रवार (d) Thursday गुरुवार
(25) Arnav\'s birthday is on Tuesday 14th March. On what day of
the week will be Pranay\'s Birthday in the same year if Pranay
was born on 13th September?
अणषव का जन्मददन मींगलवार 14 माचष को है। दयद प्रणय का जन्म 13 दसतींबर
को हुआ था तो उसी वर्ष प्रणय का जन्मददन सप्ताह में दकस ददन होगा?
SSCCGL201720AUG-S3 : 10
(a) Monday सोमवार (b) Tuesday मींगलवार
(c) Wednesday बुधवार (d) Thursday गुरुवार
Answer Key
1 A 2 C 3 C 4 C 5 C
6 C 7 B 8 A 9 D 10 A
11 A 12 C 13 A 14 C 15 D
16 A 17 C 18 A 19 B 20 A
21 A 22 B 23 D 24 A 25 C
Question: 1
A clock takes 9 seconds to strike 4 times. In order to strike 12 times at the same rate, the time taken is
एक घड़ी को 4 बार प्रहार करने में 9 सेकंड का समय लगता है। एक ही दर से 12 बार वार करने में लगने वाला समय है
(A) 27 seconds
(B) 29 seconds
(C) 33 seconds
(D) 36 seconds
Ans: C
There are 3 intervals when the clock strikes 4
Time taken in 3 intervals = 9 seconds
∴ Time taken for 1 interval = 3 seconds
In order to strike 12, there are 11 intervals,
for which the time taken is 11 x 3 seconds = 33 seconds.
Question: 2
Number of times 29th day of the month occurs in 400 consecutive year is
लगातार 400 वर्ष में महीने के 29वें दिन आने की संख्या है
(A) 4400
(B) 4497
(C) 4800
(D) 4600
Ans: B
400 consecutive years contain 97 leap years.
∴ In 400 consecutive years February has 29 days 97 times and the remaining 11 months have
29th day 400 x 11 = 4400 times
∴ 29th day of the month occurs 4400 + 97 = 4497 times.
Question: 3
Monday falls on 20th March, 1995. What was the day of 3rd November, 1994?
सोमवार 20 मार्च, 1995 को पड़ता है। 3 नवंबर, 1994 को कौन सा दिन था?
(A) Sunday
(B) Tuesday
(C) Thursday
(D) Friday
Ans: C
Number of days after 3rd November, 1994 will be
Nov. Dec. Jan. Feb. March
27 + 31 + 31 + 28 + 20 = 137 days ⇒ 19 weeks + 4 days
∴ Number of odd days = 4.
∴ The day on 3rd November, 1994 is (7 – 4) days beyond the day on 20th March, 1995. So, the
required day is Thursday.
Question: 4
What was the day of the week on 28th February, 1995?
28 फरवरी 1995 को सप्ताह का कौन सा दिन था?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
Ans: B
1600 years contain 0 odd day.
300 years contain 1 odd day.
94 years = (23 leap years + 71 ordinary years)
= (46 + 71) odd days
= 117 odd days, i.e., 5odd days.
Days from 1st January 1995 to 28th February 1995
= (31 + 28) days = 59 days
= ( 8weeks + 3 days) = 3 odd days
Total number of odd days = (0 + 1 + 5 + 3) = 9 odd days
i.e., 2 odd days.
So, the required day is Tuesday.
Question: 5
January 1, 1992 was Wednesday. What day of the week was January 1, 1993?
1 जनवरी 1992 को बुधवार था। 1 जनवरी 1993 को सप्ताह का कौन सा दिन था?
(A) Monday
(B) Tuesday
(C) Thursday
(D) Friday
Ans: D
1992 was a leap year.
Hence it had 2 odd days.
So, the first day of the year 1993 must be two days after Wednesday.
So, it was Friday.
HOME WORK
1. What is the angle between the hour hand and the minute hand at 5:10 AM?
सुबह 5:10 बजे घंटे की सूई और मिनट की सूई के बीच का कोण क्या है?
a) 355°
b) 105°
c) 195°
d) 95°
2. What is the angle between the hour hand and the minute hand at 6:30 PM?
2. शाम 6:30 बजे घंटे की सूई और मिनट की सूई के बीच का कोण क्या है?
a) 325°
b) 330°
c) 345°
d) 315°
3. What is the angle between the hour hand and the minute hand at 2:45 AM?
3. 2:45 AM पर घंटे की सूई और मिनट की सूई के बीच का कोण क्या है?
a) 227.5°
b) 127.5°
c) 172.5°
d) 272.5°
4. What is the angle between the hour hand and the minute hand at 3:20 AM?
4. सुबह 3:20 बजे घंटे की सूई और मिनट की सूई के बीच का कोण क्या है?
a) 40°
b) 20°
c) 330°
d) 320°
5. What is the angle between the hour hand and the minute hand at 4:39 PM?
5. शाम 4:39 बजे घंटे की सूई और मिनट की सूई के बीच का कोण क्या है?
a) 84.5°
b) 94.5°
c) 114.5°
d) 24.5°
6. What is the angle between the hour hand and the minute hand at 1:18 AM?
6. पूर्वाहन 1:18 बजे घंटे की सूई और मिनट की सूई के बीच का कोण क्या है?
a) 217°
b) 67°
c) 69°
d) 219°
7. What is the angle between the hour hand and the minute hand at 8:25 PM?
7. रात 8:25 बजे घंटे की सूई और मिनट की सूई के बीच का कोण क्या है?
a) 257.5°
b) 227.5°
c) 217.5°
d) 207.5°
8. What is the angle between the hour hand and the minute hand at 3:30 AM?
8. सुबह 3:30 बजे घंटे की सूई और मिनट की सूई के बीच का कोण क्या है?
a) 105°
b) 75°
c) 65°
d) 55°
9. What is the angle between the hour hand and the minute hand at 9:00 AM?
9. सुबह 9:00 बजे घंटे की सूई और मिनट की सूई के बीच का कोण क्या है?
a) 180°
b) 120°
c) 60°
d) 90°
10. What is the angle between the hour hand and the minute hand at 7:45 AM?
10. सुबह 7:45 बजे घंटे की सूई और मिनट की सूई के बीच का कोण क्या है?
a) 75°
b) 22.5°
c) 37.5°
d) 37°
11. What was the day of the week on ‘9th November 1998’?
11. '9 नवंबर 1998' को सप्ताह का कौन सा दिन था?
a) Tuesday
b) Sunday
c) Monday
d) Wednesday
12. What was the day of the week on ‘2nd July 2003’?
12. '2 जुलाई 2003' को सप्ताह का कौन सा दिन था?
a) Tuesday
b) Sunday
c) Monday
d) Wednesday
13. What was the day of the week on ‘1st January 1989’?
13. '1 जनवरी 1989' को सप्ताह का कौन सा दिन था?
a) Tuesday
b) Sunday
c) Monday
d) Wednesday
14. What was the day of the week on ‘2nd March 2018’?
14. '2 मार्च 2018' को सप्ताह का कौन सा दिन था?
a) Tuesday
b) Saturday
c) Friday
d) Wednesday
15. What was the day of the week on ‘16th February 2014’?
15. '16 फरवरी 2014' को सप्ताह का कौन सा दिन था?
a) Tuesday
b) Saturday
c) Friday
d) Sunday
16. What was the day of the week on ‘15th August 2006’?
16. '15 अगस्त 2006' को सप्ताह का कौन सा दिन था?
a) Tuesday
b) Saturday
c) Friday
d) Sunday
17. What was the day of the week on ‘19th December1937’?
17. '19 दिसंबर1937' को सप्ताह का कौन सा दिन था?
a) Tuesday
b) Saturday
c) Friday
d) Sunday
18. What was the day of the week on ‘11th May 1967’?
18. '11 मई 1967' को सप्ताह का कौन सा दिन था?
a) Wednesday
b) Thursday
c) Friday
d) Tuesday
19. What was the day of the week on ‘12th August 2017’?
19. '12 अगस्त 2017' को सप्ताह का कौन सा दिन था?
a) Sunday
b) Thursday
c) Friday
d) Saturday
20. What was the day of the week on ‘26th January 1921’?
20. '26 जनवरी 1921' को सप्ताह का कौन सा दिन था?
a) Wednesday
b) Thursday
c) Friday
d) Saturday
21. Which of the following is not a leap year?
21. निम्नलिखित में से कौन एक लीप वर्ष नहीं है?
a) 1200
b) 600
c) 1600
d) 2400
22. How many days are there in ‘y’ weeks and ‘y’ days?
22. 'y' सप्ताह और 'y' दिनों में कितने दिन होते हैं?
a) 7y2
b) 8y
c) 8y2
d) 7y
23. It was Friday on February 1, 2013. What was the day of the week on February 1, 2018?
23. 1 फरवरी, 2013 को शुक्रवार था। 1 फरवरी, 2018 को सप्ताह का कौन सा दिन था?
a) Friday
b) Wednesday
c) Thursday
d) Saturday
24. If today is Wednesday, then what will be the day after 56 days?
24. यदि आज बुधवार है, तो 56 दिनों के बाद कौन सा दिन होगा?
a) Friday
b) Wednesday
c) Thursday
d) Saturday
25. The last day of a century cannot be ___________.
25. एक सदी का अंतिम दिन ___________ नहीं हो सकता।
a) Saturday
b) Friday
c) Monday
d) Wednesday
26. If day before yesterday was Sunday, what will be the fourth day after today?
26. यदि कल से पहले का दिन रविवार था, तो आज के बाद चौथा दिन क्या होगा?
a) Saturday
b) Friday
c) Monday
d) Wednesday
27. The year next to 2014 will have the same calendar as
that of the year _________.
a) 2017
b) 2025
c) 2052
d) 2071
28. How many times in a day, do the hands of a clock coincide with each other?
28. दिन में कितनी बार घड़ी की सुइयां आपस में मिलती हैं?
a) 11
b) 48
c) 22
d) 24
29. The hour hand takes ___ fill rounds of a clock in a day.
29. घंटे की सूई एक दिन में घड़ी के ___ चक्कर लगाने में लगती है।
a) 12
b) 2
c) 24
d) 4
30. The first day of a century cannot be _______.
30. एक सदी का पहला दिन _______ नहीं हो सकता।
a) Monday
b) Saturday
c) Friday
d) Thursday
31. _________ can be the first day as well as the last day of a century year.
31. _________ एक सदी वर्ष का पहला दिन और साथ ही अंतिम दिन हो सकता है।
a) Friday
b) Monday
c) Tuesday
d) Sunday
32. If mirror shows 1:13 in a clock, then what will be actual timing?
32. यदि एक घड़ी में दर्पण 1:13 दिखाता है, तो वास्तविक समय क्या होगा?
a) 10:43
b) 10:57
c) 10:53
d) 10:47
33. The calendar for the year 2007 will be the same for the year ______.
33. वर्ष 2007 का कैलेंडर वर्ष ______ के लिए समान होगा।
a) 2011
b) 2018
c) 2028
d) 2024
34. Which of the following is not a leap year?
34. निम्नलिखित में से कौन एक लीप वर्ष नहीं है?
a) 2016
b) 1920
c) 1938
d) 2012
35. It was Tuesday on 1st January 2013, what day of the week was it on 1st January 2014?
35. 1 जनवरी 2013 को मंगलवार था, 1 जनवरी 2014 को सप्ताह का कौन सा दिन था?
a) Thursday
b) Monday
c) Wednesday
d) Friday
36. If Friday was the first day of an ordinary year, then what would be the last day of the year?
36. यदि शुक्रवार एक सामान्य वर्ष का पहला दिन होता, तो वर्ष का अंतिम दिन क्या होता?
a) Thursday
b) Monday
c) Wednesday
d) Friday
37. If Friday was the first day of a leap year, then what would be the last day of the year?
37. यदि शुक्रवार एक लीप वर्ष का पहला दिन था, तो वर्ष का अंतिम दिन क्या होगा?
a) Thursday
b) Saturday
c) Sunday
d) Friday
38. What time is shown in the mirror if real time is 8:45?
38. यदि वास्तविक समय 8:45 है तो दर्पण में कितना समय दिखाया जाता है?
a) 2:15
b) 3:15
c) 6:25
d) 7:15
39. What time is shown in the mirror if real time is 1:47?
39. यदि वास्तविक समय 1:47 है तो दर्पण में कितना समय दिखाया जाता है?
a) 10:13
b) 11:13
c) 12:13
d) 2:13
40). 44 days after Saturday will be ____________.
40)। शनिवार के 44 दिन बाद ____________ होगा।
a) Thursday
b) Monday
c) Wednesday
d) Friday
41. Which of the following years calendar will be same to the calendar for the year 2004?
41. निम्नलिखित में से कौन सा वर्ष का कैलेंडर वर्ष 2004 के कैलेंडर के समान होगा?
a) 2018
b) 2036
c) 2032
d) 2016
42. If 6th March 2005 was Monday, then what was the day on 6th March 2004?
42. यदि 6 मार्च 2005 को सोमवार था, तो 6 मार्च 2004 को कौन सा दिन था?
a) Thursday
b) Saturday
c) Sunday
d) Friday
43. If today is Wednesday, then what will be the day on 567th day?
43. यदि आज बुधवार है, तो 567वें दिन कौन-सा दिन होगा?
a) Thursday
b) Monday
c) Wednesday
d) Friday
44. If Mahesh celebrated his birthday 5 days after Suresh, whose birthday was on Friday, then on which
day of the week will Mahesh celebrate his birthday?
44. यदि महेश ने अपना जन्मदिन सुरेश के 5 दिन बाद मनाया, जिसका जन्मदिन शुक्रवार को था, तो महेश सप्ताह के किस दिन अपना जन्मदिन मनाएगा?
a) Thursday
b) Monday
c) Wednesday
d) Friday
45. Saturday, Thursday and _______ will never be the end day of a century year.
45. शनिवार, गुरुवार और _______ कभी भी एक सदी वर्ष का अंत नहीं होगा।
a) Monday
b) Wednesday
c) Tuesday
d) Friday
46. At what time are the hands of a clock together between 2 and 3?
46. घड़ी की सूइयां किस समय 2 और 3 के बीच एक साथ होती हैं?
a) 2 : 10(10/11)
b) 3 : 10(10/11)
c) 2 : 11(10/11)
d) 3 : 11(10/11)
47. At what time are the hands of a clock together between 6 and 7?
47. घड़ी की सूइयां किस समय 6 और 7 के बीच एक साथ होती हैं?
a) 7 : 32 8/11
b) 6 : 33 8/11
c) 6 : 32 8/11
d) 7 : 33 8/11
48. A clock which moves continuously fast, it lags 5 minutes on Sunday 8 AM, it is ahead 7 minute on Tuesday 8 AM. Find when the clock showed right time?
48. एक घड़ी जो लगातार तेज चलती है, वह रविवार सुबह 8 बजे 5 मिनट पीछे है, यह मंगलवार सुबह 8 बजे 7 मिनट आगे है। पता करें कि घड़ी ने कब सही समय दिखाया?
a) Saturday 4 PM
b) Saturday 4 AM
c) Monday 4 PM
d) Monday 4 AM
49. Time shown in a clock is 3:13, what time will appear in the water?
49. घड़ी में दिखाया गया समय 3:13 है, पानी में कितना समय दिखाई देगा?
a) 1:13
b) 2:17
c) 2:13
d) 3:17
50. What angle is made by minute hand in 30 seconds?
50. मिनट की सुई 30 सेकंड में कौन सा कोण बनाती है?
a) 3°
b) 29°
c) 30°
d) 2.9°
ANSWERS
1) Answer: D
2) Answer: C
3) Answer: C
4) Answer: B
5) Answer: B
6) Answer: C
7) Answer: A
8) Answer: B
9) Answer: D
10) Answer: C
11) Answer: C
12) Answer: D
13) Answer: B
14) Answer: C
15) Answer: D
16) Answer: A
17) Answer: D
18) Answer: B
19) Answer: D
Mo
nth
J
a
n
F
e
b
M
ar
A
pr
M
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A
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N
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D
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Co
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1 4 4 0 2 5 0 3 6 1 4 6
Date: 12th August 2017
Steps to find the day of the week:
Last two digit of
year
17
No. of leap year
(divisor)
Divisor = 4
Code of the month 3
Date 12
Total = (17 + 4 + 3 + 12) = 36
And 36 ÷ 7, we get 1 as remainder.
Note:
Year < 2000 – leave the remainder as it is
Year > 2000 – subtract 1 from the remainder.
So, (1 – 1) = 0
Code Day
1 Sunday
2 Monday
3 Tuesday
4 Wednesday
5 Thursday
6 Friday
0 Saturday
20) Answer: A
Mo
nth
J
a
n
F
e
b
M
ar
A
pr
M
ay
J
u
n
J
u
l
A
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S
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O
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N
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D
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Co
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1 4 4 0 2 5 0 3 6 1 4 6
Date: 26th January 1921
Steps to find the day of the week:
Last two digit of
year
21
No. of leap year Divisor = 5
(divisor)
Code of the month 1
Date 26
Total = (21 + 5 + 1 + 26) = 53
And 53 ÷ 7, we get 4 as remainder.
Note:
Year < 2000 – leave the remainder as it is
Year > 2000 – subtract 1 from the remainder.
Code Day
1 Sunday
2 Monday
3 Tuesday
4 Wednesday
5 Thursday
6 Friday
0 Saturday
21) Answer: B
Century year that is completely divisible by 400 is a leap
year.
Only 600 is not completely divisible by 400.
22) Answer: B
There are 7 days in a week.
So, no. of days in y weeks = 7y
Total number of days in y weeks and y days = (7y + y) =
8y
23) Answer: C
Number of odd days in:
2013 – 1
2014 – 1
2015 – 1
2016 – 2
2017 – 1
6 days after Friday is Thursday.
24) Answer: B
56 ÷ 7, we get 0 as remainder.
So, 56 days after Wednesday will be Wednesday again.
25) Answer: A
Last day of a century cannot be Tuesday or Thursday or
Saturday.
26) Answer: A
Day before Yesterday was Sunday.
So, today is Tuesday.
Fourth day after Monday is Saturday.
27) Answer: B
Ordinary year: To find same calendar
1
st year after a leap year Add 6
2
nd year after a leap year Add 11
3
rd year after a leap year Add 11
Leap Year:
Current leap year + 28 = Next leap year having same
calendar
As 2014 is an ordinary year, and 2012 is a leap year
which comes before 2014.
We add 11 to 2014 as 2014 is the 2nd year after a leap
year.
So, (2014 + 11) = 2025
28) Answer: C
Hands of a clock coincide once in every hour.
But, in between 11’o clock to 1’o clock, they coincide
only once.
So, the hands of a clock coincide 22 times in 24 hours.
29) Answer: B
The hour hand takes 2 fill rounds of a clock in a day.
30) Answer: C
The first day of a century cannot be – Wednesday, Friday
and Sunday.
31) Answer: B
Monday can be the first day as well as the last day of a
century year.
32) Answer: D
For every mirror image based on a clock,
If it is 12 hours clock, then subtract given timing from
11:60 hrs,
And if it is 24 hrs clock, then subtract given timing from
23:60 hrs.
Here, it is 12 - hr clock, hence, 11:60 – 1:13 = 10:47
33) Answer: B
Ordinary year: To find same calendar
1
st year after a leap year Add 6
2
nd year after a leap year Add 11
3
rd year after a leap year Add 11
Leap Year:
Current leap year + 28 = Next leap year having same
calendar
2007 is an ordinary year and 2004 is the leap year before
2007
As, 2007 is the 3rd year after a leap year, we add 11 to it
to obtain the same calendar.
(2007 + 11) = 2018.
34) Answer: C
All options except ‘1938’ are completely divisible by 4.
So it is not a leap year.
35) Answer: C
As 2013 is an ordinary year and number of odd days in
an ordinary year is 1.
So, we move 1 day ahead from Tuesday to obtain the day
of the week on 1st January 2014.
So, one day after Tuesday is Wednesday.
36) Answer: D
The first and last days of an ordinary year are same.
So, Friday will be the answer.
37) Answer: B
The last day of a leap year is one day ahead of its first
day.
So, Saturday is the answer.
38) Answer: B
For every mirror image based on a clock,
If it is 12 hours clock, then subtract given timing from
11:60 hrs,
And if it is 24 hrs clock, then subtract given timing from
23:60 hrs.
Here, it is 12 - hr clock, hence, 11:60 – 8:45 = 3:15
39) Answer: A
For every mirror image based on a clock,
If it is 12 hours clock, then subtract given timing from
11:60 hrs,
And if it is 24 hrs clock, then subtract given timing from
23:60 hrs.
Here, it is 12 - hr clock, hence, 11:60 – 1:47 = 10:13
40) Answer: B
44 ÷ 7, we get 2 as remainder.
2 days after Saturday is Monday.
41) Answer: C
Ordinary year: To find same calendar
1
st year after a leap year Add 6
2
nd year after a leap year Add 11
3
rd year after a leap year Add 11
Leap Year:
Current leap year + 28 = Next leap year having same
calendar
2004 + 28 = 2032
42) Answer: C
Odd days in 2004 = 2
But, February 2004 not included because we are
calculating from March 2004 to March 2005. So it has 1
odd day only.
So, Sunday is the correct answer.
43) Answer: C
567 ÷ 7, remainder = 0
So, it will be Wednesday after 567th day from today.
44) Answer: C
5 days after Friday is Wednesday.
45) Answer: C
Saturday, Thursday and Tuesday will never be the end
day of a century year.
46) Answer: A
Together means angle between hour and minute hand =
0°
Time = Smaller time : 2
11
(A1 ± A2) Where A1 =
Smaller value of time × 30 and A2 = Angle
So, time = 2∶
2
11
(2 × 30 ± 0)
= 2 : 2
11
× 60
= 2: 120
11
= 2 : 10
10
11
47) Answer: C
Together means angle between hour and minute hand =
0°
Time = Smaller time : 2
11
(A1 ± A2) Where A1 =
Smaller value of time × 30 and A2 = Angle
So, time = 6 ∶
2
11
(6 × 30 ± 0)
= 6 : 2
11
× 180
= 6: 360
11
= 6 : 32 8
11
48) Answer: D
Time between Sunday 8 AM to Tuesday 8 AM = 48 hour
Formula: (1st) Slow/Fast
Slow+Fast
× total
= 5/12 × 48
= 20 hour
Sunday 8 AM + 20 hour = Monday 4 AM
49) Answer: B
1. Minute is less than 30, then subtract the given time
from 5:30 hours.
2. Minute is more than 30, then subtract the given time
from 5:90 hours.
Here, time is 3:13, so 1st formula is applicable.
Time in water = (5:30 – 3:13) = 2:17
50) Answer: A
In 1 minute i.e, 60 seconds, the minute hand covers an
angle of 6°
So, in 30 seconds, the minute hand covers an angle of
Quantitative Aptitude – Clocks and Calendars – Formulas
Introduction to Quantitative Aptitude:
Quantitative Aptitude is an important section in the employment-related competitive exams in India.
Quantitative Aptitude Section is one of the key sections in recruitment exams in India including but not
limited to Banking, Railways, and Staff Selection Commission, Insurance, Teaching, UPSC and many
others. The Quantitative Aptitude section has questions related to Profit and Loss, Percentage and
Discount, Simple Equations, Time and Work and Quadratic Equations, Mensuration, Clocks and
Calendars etc.
Clocks – Important Terms:
1. What is Minute Space?
The circumference of the face or dial of the clock can be divided into 60 equal parts called minute
space
2. What is Minute Gain?
Every 60 minutes, the minute hand gains 55 minutes on the hour on the hour hand
3. What is Overlap?
In every hour, both the hands coincide once.
4. What is Straight Line?
The hands are in the same straight line when they are coincident or opposite to each other.
5. What is Clock Too Fast?
If a watch or a clock indicates 8.15, when the correct time is 8, it is said to be 15 minutes too fast.
6. What is Clock Too Slow?
If a clock indicates 45, when the correct time is 8, it is said to be 15 minutes too slow.
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
Clocks and Calendars- Aptitude Test Tricks & Shortcuts & Formulas& Examples
Quick Looks:
1. 60-minute space = 360° = 1 hour
2. 1-minute space = 6° = 1 minute
3. 5-minute space = 6° x 5 = 30° = 5 minutes
4. Right Angle or Perpendicular = 15-minute spaces apart
5. Right Angle or Perpendicular = 22 times in 12 hours or 44 times in 24 hours (1 day)
6. Straight Angle or Straight Line or 180° = 30-minute space apart
7. Straight Angle = 11 times in 12 hours or 22 times in 24 hours (1 day)
8. Angle traced by hour hand in 12 hrs = 360°
9. Angle traced by minute hand in 60 min. = 360°
10. Speed of hour hand = 0.5 dpm (degree per minute)
11. Speed of minute hand = 6 dpm
12. Angle of the hour hand from vertical at N o’clock = 30N
Concepts & Types:
Type 1: Finding the time when the angle between the two hands is given.
Type 2: Finding the angle between the 2 hands at a given time.
Type 3: Questions on clocks gaining/losing time.
S.NO. Concept
1. A clock is a complete circle having 360 degrees. It is divided into 12 equal parts i.e.
each part is 360/12 = 30°.
2. As the minute hand takes a complete round in one hour, it covers 360° in 60
minutes.
3. In 1 minute it covers 360/60 = 6°/ minute.
4. Also, as the hour hand covers just one part out of the given 12 parts in one hour.
This implies it covers 30° in 60 minutes i.e. 1⁄2° per minute.
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
5. This implies that the relative speed of the minute hand is 6 - 1⁄2 = 5 1⁄2
degrees.
6. We will use the concept of relative speed and relative distance while
solving problems on clocks
Tips:
Tip 1: It is easy to calculate the angle between the minute and the hour hand by using a
simple formula,
Angle = (X*30) -((Y*11)/2)
Tip 2: You can use a short formula to calculate the time when the angle is given
Angle = (minutes) -30 (hours)
Example 1:
Find the mirror image of the clock when the time is 01:40
A. 11:20
B. 10:22
C. 10:20
D. 11:22
Answer: C
Explanation:
We need to subtract from 12:00 or 11:60 to get mirror image time Mirror image of 01:40 =
11:60 – 01:40 = 10:20
Example 2:
Find the mirror image of the clock when the time is 02:40
A. 09:20
B. 10:22
C. 09:25
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
D. 09:22
Answer: A
Explanation: We need to subtract from 12:00 or 11:60 to get mirror image time Mirror
image of 02:40 = 11:60 – 02::40 = 09:20
Example 3:
At what time between 2 O’clock and 3 O’clock, will the minute hand and hour hand of the
clock be exactly opposite to each other?
A. 02:46
B. 02:47 6
11
C. 02:43 7
11
D. 02:47
Answer: C
Explanation:
Angle between two hands = 11
2
M – 30H where H is hours and M is Minutes
Here, H = 2 and Angle = 1800
1800 =
11
2
M – 30 X 2
11
2
M = 240
M= 480
11
= 43 7
11
Hence, the required time = 02: 43 7
11
Example 4:
At what time between 12 O’clock and 1 O’clock, will the minute hand and hour hand of the clock make
right angles?
A. 12:46
B. 12:15 6
11
C. 12:17 3
11
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
D. None of these
Answer: D
Explanation:
Angle between two hands = 11
2
M – 30H where H is hours and M is Minutes
Here, H = 2 and Angle = 900
1800 =
11
2
M – 30 X 2
11
2
M = 450
M= 900
11
= 81 7
11
Hence, the required time = 12: 81 9
11
which is 01:21 9
11
Hence, between 12 O’clock and 1 O’clock, there is no right angle
Example 5:
At what time between 2 O’clock and 3 O’clock, will the minute hand and hour hand of the clock make
right angles?
A. 02:32
B. 02:29 6
11
C. 02:27 3
11
D. 02:36
Answer: C
Explanation:
Angle between two hands = 11
2
M – 30H where H is hours and M is Minutes
Here, H = 2 and Angle = 900
1800 =
11
2
M – 30 X 2
11
2
M = 150
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
M= 300
11
= 02:27 3
11
Hence, the required time = 02: 27 3
11
Example 6:
At what time between 4 O’clock and 5 O’clock, will the minute hand and hour hand of the clock make
right angles?
A. 04:36
B. 04:38 2
11
C. 04:42 4
11
D. 04:39
Answer: B
Explanation:
Angle between two hands = 11
2
M – 30H where H is hours and M is Minutes
Here, H = 2 and Angle = 900
1800 =
11
2
M – 30 X 2
11
2
M = 210
M= 420
11
= 38 2
11
Hence, the required time = 04: 38 2
11
Example 7:
A clock shows 7 O’clock in the morning. By how much angle will the hour’s hand rotate
when the clock shows 9 O’clock in the morning.
A. 400
B. 600
C. 450
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
D. 900
Answer: c
Explanation:
In 12 hours, the hand turns 3600
Here, the difference between time = 6 hours
Then, Required angle = 360
12
x 2 = 600
Example 8:
A clock shows 6:00 in the morning. By how much angle will the hour’s hand rotate when the clock
shows 12:00 in the noon?
A. 1600
B. 1200
C. 1800
D. 1350
Answer: c
Explanation:
In 12 hours, the hand turns 3600
Here, the difference between time = 6 hours
Then, Required angle = 360
12
x 6 = 1800
Example 9:
Find the angle between the hands of the clock when the time is 10:30.
A. 1600
B. 1200
C. 1800
D. 1350
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
Answer: D
Explanation:
Required angle = 30H -
11
2
M where H is hours and M is minutes
Hence, Required angle = 30 x 10 -
11
2
x 30
= 300 – 165 = 1350
Example 10:
Check which of the following years are leap years.
A. 1800
B. 1345
C. 1678
D. none of these
Answer: D
Explanation:
1800 is century year so it must be divisible by 400 to be a leap year.
1345, 1678 are not divisible by 4
Example 11:
March 10, 2018 is Saturday. What day of the week lies on March 10, 2019?
A. Thursday
B. Friday
C. Saturday
D. Sunday
Answer: D
Explanation:
The year 2018 is non-leap year, so it has 365 days, 365 = 52 weeks + 1 odd day Hence one day
beyond Saturday is Sunday
Example 12:
Today is Saturday, after 43 days it will be?
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
A. Wednesday
B. Friday
C. Sunday
D. Tuesday
Answer: c
Explanation:
Today is Saturday. Each day of the week is repeated after every 7 days. Hence, after 42 days it will be
Saturday.
So, after 43 days, it will be Sunday
Example 13:
Sridevi was born on 13-8-1963 and died on 24-2-2018. Find her exact age?
A. 54 years 6 months 12 days
B. 54 years 5 months 22 days
C. 54 years 5 months 12 days
D. 54 years 6 months 22 days
Answer: A
Explanation:
13-8-1963 to 12-8-2017 = 54 years 13-8-2017 to 12-2-2018 = 6 months 13-2-2018 to 24-
2-2018 = 12 days
Example 14:
Find the average number of days per month in the year 1994?
A. 30.4266
B. 30.4166
C. 30.4066
D. 30.3966
Answer: B
Explanation:
1994 has 365 days
average days per month = 365
12
= 30.4166
Example 15:
If 1st January of 1996 was Monday, then How many Tuesdays did 1996 have?
A. 53
B. 52
C. 51
D. cannot be determined
Answer: A
Explanation:
1996 has 366 days = 52 weeks + 2days If 1st Jan 1996 was Monday, it would have 53
Mondays and 53 Tuesdays.
Example 16:
Find the angle between the minute hand and hour hand of a clock when the time is 7.20?
Explanation:
Angle traced by the hour hand in 12 hours = 360 degrees.
• Angle traced by it in 7 hrs. 20 min i.e. 22
3
hrs. = [(360
12
) * (22
3
)] = 220 degrees
• Angle traced by minute hand in 60 min = 360 deg.
• Angle traced by it in 20 min = [(360
12
) * 60] = 120 deg.
• Therefore, required angle = (220 - 120) = 100deg.
Example 17:
The minute hand of a clock overtakes the hour’s hand at intervals of 65 min of the correct time. How much of
the day does the clock gain or lose?
Explanation: In a correct clock, the minute hand gains 55 min. spaces over the hour hand in 60 minutes. To be
together again, the minute hand must gain 60 minutes over the hour hand.
• 55 minutes are gained in 60 min.
• 60 min. are gained in [(60
55
) * 60] min = 65 5
11
min.
• But they are together after 65 min.
• Therefore, gain in 65 minutes = (65 5
11
- 65) = 5
11
min.
• Gain in 24 hours = [( 5
11
) * (60∗24
65
] = 10 10
43
min.
• Therefore, the clock gains 10 10
43
minutes in 24 hours
Example 18:
A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours. What will be the true time when the clock
indicates 1 p.m. on the following day?
Explanation:
Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.
• 24 hours 10 min. of this clock = 24 hours of the correct clock.
•
1455
6
hrs of this clock = 24 hours of the correct clock.
• 29 hours of this clock = [24 * ( 6
145
) * 29] hrs of the correct clock
• = 28 hrs 48 min of the correct clock.
• Therefore, the correct time is 28 hrs 48 min. after 8 a.m.
• This is 48 min. past 12.
Example 19:
At what time between 2 and 3 O’ clock will the hands of a clock together?
Explanation:
At 2 O’ clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10 min space apart. To be together,
the minute hand must gain 10 minutes over the other hand. Now, 55 minutes are gained by it in 60 min.
• Therefore, 10 min will be gained in [(660
55
) * 10] min = 10 106
11
min.
• Therefore, the hands will coincide at 10 10
11
min. past 2.
Example 20:
How many times do the hands of a clock coincide in a day?
A. 20
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
B. 21
C. 22
D. 24
Answer: C
Explanation:
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once,
i.e., at 12 o'clock).
AM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
PM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
7:38
8:44
9:49
10:55
The hands overlap about every 65 minutes, not every 60 minutes.
The hands coincide 22 times in a day.
Example 21:
How many times in a day, the hands of a clock are straight?
A. 22
B. 24
C. 44
D. 48
Answer: C
Explanation:
In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Example 22:
How many times are the hands of a clock at right angle in a day?
A. 22
B. 24
C. 44
D. 48
Answer: C
Explanation:
In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
Example 23:
How many times in a day, are the hands of a clock in straight line but opposite in direction?
A. 20
B. 22
C. 24
D. 48
Answer: B
Explanation:
The hands of a clock point in opposite directions (in the same straight line) 11 times in
every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o’clock
only).
Example 24:
What is the angle between the two hands of a clock when the time shown by the clock is 6.30 p.m.?
A. 00
B. 50
C. 30
D. 150
Answer: D
Explanation:
q =
11
12
m – 30h
=
11
12
*30 - 30 *6
= 150
Example 25:
By how many degrees does the minute hand move in the same time, in which the hour hand move by
280?
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
A. 168
B. 336
C. 196
D. 376
Answer: B
Explanation:
28*2 *6 = 3360
Calendars – Important Terms:
1. What is an ordinary year?
The year which is not a leap year is called an ordinary year. An ordinary year has 365 days.
2. What is Leap Year?
A leap year has 366 days.
Every year divisible by 4 is a leap year, if it is not a century.
Every 4th century is a leap year and no other century is a leap year.
3. What is meant by odd days?
We are supposed to find the day of the week on a given date. For this, we use the concept of 'odd
days'. In a given period, the number of days more than the complete weeks are called odd days.
Quick Looks:
A leap year has 366 days
Every year divisible by 4 is a leap year, if it is not a century.
Every 4th century is a leap year and no other century is a leap year.
Counting odd days
1 ordinary year ≡ 365 days ≡ (52 weeks + 1 day)
Hence number of odd days in 1 ordinary year= 1.
1 leap year = 366 days = (52 weeks + 2 days)
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
Hence number of odd days in 1 leap year= 2.
100 years = (76 ordinary years + 24 leap years)
= (76 x 1 + 24 x 2) odd days
= 124 odd days.
= (17 weeks + 5 days)
= 5 odd days.
Hence number of odd days in 100 years = 5.
Number of odd days in 200 years = (5 x 2) = 10 = 3 odd days
Tricks:
100 years give us 5 odd days as calculated above.
200 years give us 5 x 2 = 10 – 7 (one week) 3 odd days.
300 years give us 5 x 3 = 15 – 14 (two weeks) 1 odd day.
400 years give us {5 x 4 + 1 (leap century)} – 21} (three weeks) 0 odd days.
Month of January gives us 31 – 28 = 3 odd days.
Month of February gives us 28 – 28 = 0 odd day in a normal year and 1 odd day in a leap year and
so on for all the other months.
Note:
When you count from the beginning i.e. 1st January, 0001
1. 1 odd day mean – Monday
2. 2 odd days mean – Tuesday
3. 3 odd days mean – Wednesday and so on 6 odd days means Saturday.
Example 1:
Today is Monday. After 61 days, it will be:
A. Tuesday
B. Monday
C. Sunday
D. Saturday
Answer: D
Explanation:
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
Each day of the week is repeated after 7 days. So, after 63 days, it will be Monday.
Example 2:
It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
A. Monday
B. Friday
C. Sunday
D. Tuesday
Answer: B
Explanation:
On 31st December, 2005 it was Saturday.
Number of odd days from 2006 to 2009 = (1 + 1 + 2 + 1) = 5 days.
On 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday
Example 3:
What was the day of the week on, 16th July, 1776?
A. Tuesday
B. Wednesday
C. Monday
D. Saturday
Answer: A
Explanation:
16th July, 1776 = (1775 years + Period from 1st Jan, 1776 to 16th July, 1776)
Counting of odd days :
1600 years have 0 odd day.
100 years have 5 odd days.
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
75 years = (18 leap years + 57 ordinary years) = [(18 x 2) + (57 x 1)] = 93 (13 weeks + 2
days) = 2 odd days
1775 years have (0 + 5 + 2) odd days = 7 odd days = 0 odd day.
Jan Feb Mar Apr May Jun Jul
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days= (28 weeks + 2 days)
Total number of odd days = (0 + 2) = 2.
Required day was 'Tuesday'.
Example 4:
What will be the day of the week 15th August, 2010?
A. Sunday
B. Saturday
C. Wednesday
D. Monday
Answer: A
Explanation:
15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 = 4 odd days.
Jan. Feb. Mar. Apr. May. Jun. Jul. Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days = (32 weeks + 3 days) = 3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 = 0 odd days.
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
Given day is Sunday
Example 5:
What was the day of the week on 17th June, 1998?
A. Monday
B. Tuesday
C. Wednesday
D. Friday
Answer: A
Explanation:
17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)
Odd days in 1600 years = 0
Odd days in 300 years = 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years (24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March. April. May. June.
(31 + 28 + 31 + 30 + 31 + 17) = 168 days
168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.
Example 6:
How many days are there in x weeks’ x days?
A. 7x * x
B. 8x
C. 14x
D. 7
Answer: B
Explanation:
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
x weeks’ x days = (7x + x) days = 8x days.
Example 7:
If 6th March, 2005 is Monday, what was the day of the week on 6th March, 2004?
A. Sunday
B. Saturday
C. Tuesday
D. Wednesday
Answer: B
Explanation:
The year 2004 is a leap year. So, it has 2 odd days.
But, Feb 2004 not included because we are calculating from March 2004 to March 2005.
So it has 1 odd day only.
The day on 6th March, 2005 will be 1 day beyond the day on 6th March, 2004.
Given that, 6th March, 2005 is Monday.
6th March, 2004 is Sunday (1 day before to 6th March, 2005).
Example 8:
On what dates of April, 2001 did Wednesday fall?
A. 2nd,9th,16th,23rd
B. 4th,11th,18th,25th
C. 12th,18th,27th,6th
D. 1st,8th,15th,22nd
Answer: B
Explanation:
We shall find the day on 1st April, 2001.
1st April, 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001)
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
Odd days in 1600 years = 0
Odd days in 400 years = 0
Jan. Feb. March April
(31 + 28 + 31 + 1) = 91 days 0 odd days.
Total number of odd days = (0 + 0 + 0) = 0
On 1st April, 2001 it was Sunday.
In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th.
Example 9:
On 8th Dec, 2007 Saturday falls. What day of the week was it on 8th Dec, 2006?
A. Saturday
B. Friday
C. Monday
D. Tuesday
Answer: B
Explanation:
The year 2006 is an ordinary year. So, it has 1 odd day.
So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.
But, 8th Dec, 2007 is Saturday
S0, 8th Dec, 2006 is Friday.
Example 10:
On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
A. Tuesday
B. Saturday
C. Friday
D. Sunday
Answer: B
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
Explanation:
The year 2004 is a leap year. It has 2 odd days.
The day on 8th Feb, 2004 is 2 days before the day on 8th Feb, 2005.
Hence, this day is Sunday
Example 11:
January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
A. Monday
B. Tuesday
C. Wednesday
D. Sunday
Answer: B
Explanation:
The year 2007 is an ordinary year. So, it has 1 odd day.
1st day of the year 2007 was Monday
1st day of the year 2008 will be 1 day beyond Monday
Hence, it will be Tuesday.
Example 12:
Which two months in a year have the same calendar?
A. October, December
B. April, November
C. June, October
D. April, July
Answer: D
Explanation:
If the period between the two months is divisible by 7, then that two months will have
the same calendar.
(a). Oct + Nov = 31 + 30 = 61 (not divisible by 7)
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
(b). Apr + May + Jun + Jul + Aug + Sep + Oct = 30 + 31 + 30 + 31 + 31 + 30 + 31 = 214 (not
divisible by 7)
(c). Jun + July + Aug + Sep = 30 + 31 + 31 + 30 = 122 (not divisible by 7)
(d). Apr + May + June = 30 + 31 + 30 = 91 (divisible by 7)
Hence, April and July months will have the same calendar.
Example 13:
The maximum gap between two successive leap year is?
A. 4
B. 8
C. 2
D. 1
Answer: D
Explanation:
This can be illustrated with an example.
Ex: 1896 is a leap year. The next leap year comes in 1904 (1900 is not a leap year).
Example 14:
How many weekends in a year?
A. 52
B. 53
C. 103
D. 104
Answer: A
Explanation:
Weekend means Saturday & Sunday together. In total we have 52 weeks in a year. So
there are 52 weekends in a year.
In normal we have 104 Weekend Days.
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
We know that an Each normal year has 365 days or 52 weeks plus one day, and each
week has two weekend days, which means there are approximately 104 weekend days
each year.
Whereas in a leap year we have 366 days it adds one more day to the year. And what
makes the change is the starting day of the year.
Example 15:
26 January 1950 which day of the week?
A. Monday
B. Wednesday
C. Thursday
D. Tuesday
Answer: A
Explanation:
Odd days --> days more than complete weeks
Number of odd days in 400/800/1200/1600/2000 years are 0.
Hence, the number of odd days in first 1600 years are 0.
Number of odd days in 300 years = 1
Number of odd days in 49 years = (12 x 2 + 37 x 1) = 61 days = 5 odd days
Total number of odd days in 1949 years = 1 + 5 = 6 odd days
Now look at the year 1950
Jan 26 = 26 days = 3 weeks + 5 days = 5 odd days
Total number of odd days = 6 + 5 = 11 => 4 odd days
Odd days: -
0 = Sunday ;
1 = monday ;
2 = tuesday ;
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
3 = wednesday ;
4 = thursday ;
5 = friday ;
6 = saturday
Example 16:
How many leap years does 100 years have?
A. 25
B. 24
C. 4
D. 26
Answer: A
Explanation:
Given year is divided by 4, and the quotient gives the number of leap years.
Here, 100%4 = 25.
But, as 100 is not a leap year => 25 - 1= 24 leap years.
Example 17:
How many leap years do 300 years have?
A. 75
B. 74
C. 72
D. 73
Answer: A
Explanation:
Given year is divided by 4, and the quotient gives the number of leap years.
Here, 300%4 = 75.
But, as 100,200 and 300 are not leap years => 75 - 3= 72 leap years.
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
Example 18:
The year next to 2005 will have the same calendar as that of the year 2005?
A. 2016
B. 2022
C. 2011
D. None
Answer: A
Explanation:
Repetition of leap year ===> Add +28 to the Given Year.
Repetition of non-leap year
Step 1: Add +11 to the Given Year. If Result is a leap year, Go to step 2.
Step 2: Add +6 to the Given Year.
Given Year is 2005, Which is a non-leap year.
Step 1: Add +11 to the given year (i.e. 2005 + 11) = 2016, Which is a leap year.
Step 2: Add +6 to the given year (i.e. 2005 + 6) = 2011
Therefore, the calendar for the year 2005 will be same for the year 2011
Example 19:
If today is Saturday, what will be the day 350 days from now?
A. Saturday
B. Friday
C. Sunday
D. Monday
Answer: A
Explanation:
350 days = (350=
7
=50 weeks) i.e. No odd days,
So it will be a Saturday.
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
Example 20:
Prove that any date in March of a year is the same day of the week corresponding date in November
that year.
A. Same day
B. Not same day
C. Next day
D. Previous day
Answer: A
Explanation:
We will show that the number of odd days between last day of February and last day of
October is zero.
March April May June July Aug. Sept. Oct.
31 + 30 + 31 + 30 + 31 + 31 + 30 + 31
= 241 days = 35 weeks = 0 odd day., Number of odd days during this period = 0.
Thus, 1st March of a year will be the same day as 1st November of that year. Hence, the
result follows
Example 21:
If Feb 12th,1986 falls on Wednesday then Jan 1st,1987 falls on which day?
A. Wednesday
B. Tuesday
C. Thursday
D. Friday
Answer: C
Explanation:
First, we count the number of odd days for the left over days in the given period.
Here, given period is 12.2.1986 to 1.1.1987
Feb Mar Apr May June July Aug Sept Oct Nov Dec Jan
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
16 31 30 31 30 31 31 30 31 30 31 1 (left days)
2 + 3 + 2 + 3 + 2 + 3 + 3 + 2 + 3 + 2 + 3 + 1(odd days) = 1 odd day
So, given day Wednesday + 1 = Thursday is the required result.
Example 22:
If Aug 15th,2012 falls on Thursday then June 11th,2013 falls on which day?
A. Wednesday
B. Saturday
C. Monday
D. Tuesday
Answer: C
Explanation:
First, we count the number of odd days for the left over days in the given period.
Here, given period is 15.8.2012 to 11.6.2013
Aug Sept Oct Nov Dec Jan Feb Mar Apr May Jun
16 30 31 30 31 31 28 31 30 31 11(left days)
2 + 2 + 3 + 2 + 3 + 3 + 0 + 3 + 2 + 3 + 4 (odd days) = 6 odd days
So, given day Thursday + 6 = Wednesday is the required result.
Example 23:
The calendar for the year 1988 is same as which upcoming year?
A. 2012
B. 2014
C. 2016
D. 2010
Answer: C
Explanation:
We already know that the calendar after a leap year repeats again after 28 years.
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
Here 1988 is a Leap year, then the same calendar will be in the year = 1988 + 28 = 2016.
Example 24:
If every seconds Saturday and all Sundays are holidays in a 30 days month beginning on Saturday, then
how many working days are there in that month? (Month starts from Saturday)
A. 25
B. 22
C. 24
D. 23
Answer: D
Explanation:
As month begins on Saturday, so 2nd, 9th, 16th, 23rd, 30th days will be Sundays. While
8th and 22nd days are second Saturdays. Thus, there are 7 holidays in all.
Hence, no. of working days = 30 – 7 =23
Example 25:
Second & fourth Saturdays and every Sunday is a holiday. How many working days will be there in a
month of 31 days beginning on a Friday?
A. 24
B. 23
C. 22
D. 25
Answer: D
Explanation:
Given that the month begins on a Friday and has 31 days
Sundays = 3rd, 10th, 17th, 24th, 31st
=> Total Sundays = 5
Every second & fourth Saturday is holiday.
2nd & 4th Saturday in every month = 2
Total days in the month = 31
Quantitative Aptitude – Clocks and Calendars – Formulas E-book
Total working days = 31 - (5 + 2) = 24 days.
Question: 1
The day on 5th March of a year is the same day on what date of the
same year?
(A) 5th August
(B) 5th October
(C) 5th November
(D) 5th December
Ans: C
Since any date in March is the same day of the week as the corresponding date in November of
that year, so the same day falls on 5th November.
Question:2
January 7, 1992 was Tuesday. Find the day of the week on the
same date after 5 years, i.e., on January 7, 1997?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Friday
(E) Friday
Ans: B
During the interval we have two leap years as 1992 and 1996 and it contains February of both
these years.
∴, The interval has (5 + 2) = 7 odd days or 0 odd day.
Hence, January 7, 1997 was also Tuesday.
Question: 3
My watch gains 5 minutes, in every hour. How many degrees the
second hand moves in every minute?
(A) 375°
(B) 380°
(C) 385°
(D) 390°
Ans: D
Since minute hand gains 5 minutes in every 60 minutes.
Second hand gains 5 seconds in every 60 seconds
In every 60 seconds true time, it moves 65 seconds or 65 x 6° = 390°
Question: 4
What was the day of the week of 1st January 2001?
(A) Tuesday
(B) Wednesday
(C) Friday
(D) Sunday
Ans: D
2000 years have 0 odd days.
1
st January, 2001 will be Sunday.
Question: 5
May 6, 1993 was Thursday. What day of the week was on May 6,
1992?
(A) Tuesday
(B) Wednesday
(C) Friday
(D) Saturday
Ans: A
1992 was a leap year, so it had 2 odd days.
So, the day on May 1993 is 2 days beyond the day on M1ay 6, 1992.
But, on May 6, 1993 it was Thursday.
So, on May 6, 1992 it was Tuesday.
1. If the two hands in a clock are 3 minutes
divisions apart, then the angle between them is
(a) 3° (b) 18° (c) 24° (d) 60°
2. At what approximate time between 4 and 5 am
will the bands of a clock be at right angle?
(a) 4:40 am (b) 4:38am
(c) 4:35 am (d) 4:39 am
3. What will be the acute angle between hands of
a clock at 2: 30?
(a) 105° (b) 115° (c) 95° (d) 135°
4. In 16 minutes, the minute hand gains over the
hour .hand by
(a) 16° (b) 80° (c) 88° (d) 96°
5. A clock is set right at 1 p.m. If it gains one
minute in an hour, then what is the true time
when the clock indicates 6 p.m. in the same
day?
(a) 55 5
61
minutes past 5
(b) 5 minutes past 6
(c) 5 minutes to 6
(d) 59 1
64
minutes past 5
6. Two clocks were set right at noon on Sunday.
One gains 2 min and the other loses 3 min in
24 hours. What will be the true time when the
first clock indicates 3 pm on Wednesday?
(a) 2:38 pm (b) 2:54 pm
(c) 2:23 pm (d) 2:48 pm
7. At what time between 9’O clock and 10'O
clock will the hands of a clock point in the
opposite directions?
(a) 16 4
11
minutes past 9
(b) 16 4
11
minutes past 8
(c) 55 5
61
minutes past 7
(d) 55 5
61
minutes to 8
8. A clock gains 15 minutes per day. It is set
right at 12 noon. What time will it show at
4.00 am, the next day?
(a) 4:10 am (b) 4:45am
(c) 4:20 am (d) 5:00am
9. Find the exact time between 7 am and 8 am
when the two hands of a watch meet?
(a) 7 hrs 35 min (b) 7 hrs 36.99 min
(c) 7 hrs 38.18min (d) 7 hrs 42.6mm
10. In a watch, the minute hand crosses the hour
hand for the third time exactly after every 3
hrs., 18 min., 15 seconds of watch time. What
is the time gained or lost by this watch in one
day?
(a) 14 min. 10 seconds lost
(b) 13 min. 50 seconds lost
(c) 13min. 20 seconds gained
(d) 14 min. 40 seconds gained
11. At what time between 3 and 4 ’O clock, the
hands of a clock coincide?
(a) 16 4
11
minutes past 3
(b) 15 5
61
minutes past 3
(c) 15 5
60
minutes to 2
(d) 16 4
11
minutes to 4
12. A watch which gains uniformly is 2 minutes
low at noon On Monday and is 4 min 48 sec,
fast at 2 p.m. on the following Monday. When
was it correct?
(a) 2 p.m. on Tuesday
(b) 2 p.m. on Wednesday
(c) 3 p.m. on Thursday
(d) 1 p.m. on Friday
13. If a clock strikes 12 in 33 seconds, it will
strike 6 in how many seconds?
(a) 33
2
(b) 15 (c) 12 (d) 22
14. A watch which gains 5 seconds in 3 minutes
was set right at 7 a.m. In the afternoon of the
same day, when the watch indicated quarter
past 4 O’clock, the true time is
(a) 4 p.m. (b) 59 7
12
minutes past 3
(c) 58 7
11
minutes past 3
(d) 2
3
11
minutes past 4
15. At what time between 8 and 9 o’clock will the
hands of a watch be in straight line but not
together?
(a) 10 11
10
min. past 8 (b) 10 10
11
min. past 8
(c) 11 10
11
min. past 8 (d) 12 10
11
min. past 8
16. At what time between 5.30 and 6 will the
hands of a clock be at right angles?
(a) 43 5
11
min. past 5 (b) 43 7
11
min.past 5
General Intelligence & Reasoning –
Clock And Calendar
(c) 40 min. past 5 (d) 45 min. past 5
17. Find the angle between the hour hand and the
minute hand o f a clock when the time is 3.2 5.
(a) 45° (b) 37 1
2
° (c) 47 1
2
° (d) 46°
18. How much does a watch lose per day, if its
hands coincide every 64 minutes?
(a) 32 8
11
min. (b) 36 5
11
min.
(c) 90 min. (d) 96 min.
19. An accurate clock shows 8 O’clock in the
morning. Through how many degrees will the
hour hand rotate when the clock shows 2
O’clock in the afternoon?
(a) 144° (b) 150° (c) 168° (d) 180°
20. A clock is set right at 5 a.m. The clock loses
16 min. in 24 hours. What will be the true time
when the clock indicates 10 p.m. on the 4th
day?
(a) 11p.m. (b) 10 p.m. (c) 9 p.m. (d) 8 p.m.
21. The reflex angle between the hands of a clock
at 10:2: 5 is?
(a) 180° (b) 1921
2
° (c) 195° (d) 1971
2
°
22. A clock gains 5 minutes, in 24 hours. It was
set right at 10 a.m. on Monday. What will be
the true time when the clock indicates 10:30
a.m. on the next Sunday?
(a) 10 a.m.
(b) 11 a.m.
(c) 25 minutes past 10 a.m.
(d) 5 minutes to 11 a.m.
23. At what angle the hands of a clock are inclined
at 15 minutes past 5 ?
(a) 721
2
° (b) 64° (c) 581
2
° (d) 67 1
2
°
24. What will be the day of the week on 1st
January, 2010?
(a) Friday (b) Saturday (c) Sunday (d) Monday
25. The calendar for the year 2005 is the same as
for the year:
(a) 2010 (b) 2011
(c) 2012 (d) 2013
26. If 09/12/2001 happens to be Sunday, then
09/12/1971 would have been at
(a) Wednesday (b) Tuesday
(c) Saturday (d) Thursday
27. Find the day of the week on 16th July, 1776.
(a) Tuesday (b) Wednesday
(c) Monday (d) Thursday
28. On January 12, 1980, it was Saturday. The day
of the week on January 12, 1979 was –
(a) Saturday (b) Friday
(c) Sunday (d) Thursday
29. The year next to 1991 having the same
calendar as that of 1990 is-
(a) 1998 (b) 2001 (c) 2002 (d) 2003
30. Today is Monday. After 61 days it will be:
(a) Wednesday (b) Saturday
(c) Tuesday (d) Thursday
ANSWER KEY
1 (b) 5 (a) 9 (c) 13 (b) 17 (c 21 (d) 25 (c) 29 (c)
2 (b) 6 (b) 10 (b) 14 (a) 18 (a) 22 (a) 26 (d) 30 (b)
3 (a) 7 (a) 11 (a) 15 (b) 19 (d) 23 (d) 27 (a)
4 (c) 8 (a) 12 (b) 16 (b) 20 (a) 24 (c) 28 (b)
General Intelligence & Reasoning –
Clock And Calendar
HINTS & EXPLANATIONS
1. (b) In a clock, each minute makes 6°
∴ 3 minutes will make 6×3=18°
2. (b) Here H ×30 = 4 × 30 = 120°.
(Since initially the hour hand is at 4. ∴H
= 4). Required angle A = 90° and since,
H × 30 > A° so, there will be two
timings.
Required time T = 2
11
(H × 30 ± A)
minutes past H.
∴One timing = 2
11
(4 × 30 + 90) minutes
past 4
= 38 2
11
minutes past 4.
Or 4: 38 approx.
3. (a) At 2'O Clock, Minute Hand will be
10×6 = 60° behind the Hour Hand.
In 30 minutes, Minute Hand will gain
5
1
2
° × 30
= 150 + 15 = 165°
∴Angle between Hour Hand and Minute
Hand = 165 -60 = 105°
4. (c) In 1 hour, the minute hand gains
330° over the hour hand.
i.e. in 60 minute, the minute hand gains
330° over the hour hand.
∴In 16 minutes, the minute hand gains
over the hour hand by 330°
60
× 16° = 88
5. (a) Time interval indicated by incorrect
clock = 6 p.m -1 p.m= 5 hrs.
Time gained by incorrect clock in one
hour
=+1 min= +
1
60
hr.
Using the formula,
True time interval
Time interval in incorrect clock
=
1
1 + hour gained in 1 hour by incorrect clock
⇒
True time interval
5
=
1
1+
1
60
⇒ True time interval = 5×60
61
= 4
56
61
∴ True time = 1 p. m + 4 56
61
hrs.
= 5 p.m + 56
61
hrs. = 5 pm + 56
61
×60 min.
= 55 5
61
minutes past 5.
6. (b) Time from noon on Sunday to 3 pm
on Wednesday = 75 hours.
24 hours 2 minutes of the first clock
= 24 hours of the correct one.
⇒ 1 hour of the first clock = 24 ×
(30/721) hours of correct one.
⇒75 ours of the first clock
= 24 ×30 × (75/721) hours of correct
one
= 54000/721 hours = 74 hours 53.7 min
Hence the answer is 2:54 PM
7. (a) AT 9’O clock, the Minute Hand is
ahead of Hour H and by 45 minutes. The
hands will be opposite to each other
when there is a space of 30 minutes
between them.
This will happen when the Minute Hand
gains 15 minutes’ space over Hour
Hand.
Time taken by Minutes Hand to gain 15
minutes
= 15 × 1 +
1
11 = 15 +
15
11
= 15 +
1
4
11
= 16 4
11
minutes.
Hence the Hands are opposite to each
other at 16 4
11
minutes past 9.
8. (a) The clock gains 15 min in 24 hours.
Therefore, in 16 hours, it will gain 10
minutes.
Hence, the time shown by the clock will
be 4.10 am.
9. (c) 55 min spaces are gained in 60 min
⇒35 min spaces will be gained in 38.18
min;
⇒Answer = 7hrs + 38.18 min
General Intelligence & Reasoning –
Clock And Calendar
10. (b) In a watch than is running correct the
minute hand should cross the hour hand
once in every 65 + 5
11
min.
So they should ideally cross 3 times
once in
3 ×
720
11 =
−2160
11
min = 196.36
minutes
But in the watch under consideration,
they meet after every 3hr, 18 min and 15
seconds,
i.e., 3 × 60 + 18 +
15
60 =
793
4
min.
Thus, our watch is actually losing time
(as it is slower than the normal watch).
Hence when our watch elapsed
1440 ×
196.36
198.25 = 1426.27
Hence the amount of time lost by our
watch in one day
= (1440 - 1426.27) = 13.73 i.e. 13 min
and 50s (approx).
11. (a) Since, in one hour, two hands of a
clock coincide only once, so, there will
be value.
Required time T= 2
11
(H×30 + A°)
minutes past H.
Here H= initial position of hour hand=3
(Since 3 O’clock)
A° = required angle = 0° (Since it
coincides)
T =
2
11
(3×30 + 0) minute spast 3
= 1614
11
minutes past 3.
12. (b) Time from 12p.m. on Monday to 2
p.m. on the following Monday = 7 days
2 hours =, 1.70 hours.
The watch gains 2 + 4
4
5
min.
or
34
5
min in 170 hrs.
Now, 34
5
min are gained in 170 hrs.
∴ 2 min are gained in 170 ×
5
34
×
2 hrs = 50 hrs.
∴ Watch is correct 2 days 2 hrs, after 12
p.m. on Monday i.e. it will be correct at
2 p.m. on Wednesday,
13. (b) In order to strike 12, there are 11
intervals of equal time =
33
11
=3 seconds
each
Therefore, to strike 6 it has 5 equal
intervals, it requires 5×3=15 sec.
14. (a)
15. (b)
16. (b)
17. (c)
18. (a)
19. (d)
20. (a) Time from 5 a.m. on a day to 10 p.m.
on 4th day is 89 hours.
Now, 23hrs 44 min of this clock are the
same as 24 hours of the correct clock.
i.e., 356
15
hrs. of this clock = 24hrs. of
correct clock.
∴89 hrs. of this clock =
24×15
356
× 89
hrs. of correct clock
= 90hrs of correct clock.
So, the correct time is 11 p.m.
21. (d) Angle traced by hour hand in 125
12
hrs.
=
360
12
×
125
25
°
= 312 1
2
°
Angle traced by minute hand in 25 min.
=
360
12
× 25
°
= 150°
∴ Reflex angle = 360 - 312 1
2
−
150°=19712°
22. (a) Time between 10 a.m. on Monday to
10:30 a.m. on Sunday = 144 1
2
hours.
24 1
2
hours of incorrect clock = 24 hours
of correct time.
∴ 144 1
2
hours of incorrect clock = x
hours of correct time.
∴x =
1441
2
×24
241
2
= 144 hours i.e.,
The true time is 10 a.m. on Sunday.
23. (d) At 15 minutes past 5, the minute
hand is at 3 and hour hand slightly
advanced from 5. Angle between their
3rd and 5th position.
Angle through which hour hand shifts in
15 minutes is 15 ×
1
2
°
= 7
1
2
°
∴ Required angle = 60 + 7
1
2
°
= 67 1
2
°
24. (c)
25. (c)
26. (d)
27. (a)
28. (b)
29. (c) .
30. (b)
कैलेंडर से संबंधित प्रश्नों को हल करने की विधि
Tricks to solve Calendar Question in easy way
कैलेंडर (Calendar) से संबंधित प्रश्न सभी एग्जाम में पूछे जाते हैं और इन को हल करना बहुत ही आसान है आप कुछ बातों का ध्यान रखना होगा जिससे आप आसानी से कैलेन्डर से संबंधित प्रश्न हल सकते है
Important Fact
- दिन (Day)– दिन की संख्या 7 होती है रविवार , सोमवार, मंगलवार, बुधवार ,गुरुवार ,शुक्रवार ,शनिवार
- महीने(Months ) – महीने की संख्या 12 होती है जनवरी ,फरवरी, मार्च अप्रैल, मई, जून, जुलाई, अगस्त, सितंबर, अक्टूबर, नवंबर, दिसंबर
Remembers
- जनवरी , मार्च , मई, जुलाई, अगस्त, अक्टूबर एवं दिसंबर महीने में 31 दिन होते है
- अप्रैल, जून, सितंबर एवं नवंबर महीने में 30 दिन होते है
- फरवरी माह 28 या 29 दिन का होता है
- वर्ष (Year )- 1 वर्ष में 365 दिन या 366 दिन होते हैं इसी आधार पर वर्ष को दो भागों में बांटा गया है
- साधारण वर्ष – इसमे 365 दिन होते है
- लीप वर्ष– इसमे 366 दिन होते है गए लीप वर्ष इस वर्ष होता है जिसमें चार का पूरा पूरा भाग चलाजाता है उसे एक लीप वर्ष कहते हैं
जैसे- 2000
इसमें हम 4 का भाग देंगे तो 500 बार पूरा पूरा भाग चल जाएगा शेषफल कुछ भी नहीं बचता है इसलिए यह लीप वर्ष है
यदि शेषफल बचता है तो वह साधारण वर्ष होगा
जैसे -2002
इसमें 4 का भाग देने पर भागफल 500 आता है तथा शेषफल 2 बच जाता है इसलिए यह साधारण वर्ष होगा
- शताब्दी वर्ष(Centenary year ) – वर्ष में 100 से पूरा पूरा भाग जाता लगता है उसे शताब्दी वर्ष कहते हैं जैसे 1500, 2100
- विषम दिन(Odd day)– किसी भी माह , वर्ष आदि के दिनों की संख्या में 7 से भाग देने पर जो बचता है वह उसका विषम दिन होता है
जैसे -जनवरी के महीने में विषम दिनों की संख्या जनवरी में दिनों की संख्या – 31
अब 31 को 7 से भाग देने पर 3 शेष बचता है
जनवरी में विषम संख्या -3
Remember- कैलेंडर से संबंधित प्रश्नों को हल करने के लिए विषम दिन की अवधारणा को जाना बहुत ही जरुरी है
जैसे आपको 15 दिन में विषम दिनों की संख्या पता करना है तो 7 का भाग दे दो
15/7 =2 भागफल 1 शेषफल
जो शेषफल होगा वो ही विषम दिनों की संख्या होगी
ऐसे हो हम ही हम कितने भी वर्ष और दिनों में विषम संख्या ज्ञात कर सकते हैं
विषम दिनों की संख्या का प्रयोग किसी भी तिथि वार को कौन सा दिन होगा यह ज्ञात करने के लिए प्रयोग किया जाता है
प्रश्नों को हल करने की विधि (Method of solving problems)-
नीचे दी गई विधि का प्रयोग करके आप बहुत ही आसानी से प्रश्नों को हल कर सकते हैं
वर्ष का संख्या ज्ञात करना (Find out the number of years )-1999 में 99 में लिखा जाएगा जैसे 1987 इसमें इस केवल 87 लिखा जाएगा
2001=101
2000 से जब भी हम वर्ष की संख्या ज्ञात करेंगे तो उसमें हम सो से शुरु करके करेंगे जैसे 2001 – 101
2002- 102
2005- 105
2017- 117
ऐसे ही आगे भी
Remember- वर्ष 1999 तक वर्ष का दहाई का अंक दिया जाता है जबकि 2000 और उसके बाद के वर्षों के लिए सैकड़ों संख्या लिया जाता है
महीने का कोड याद करना( Remember the code of the month )-
| महीना | जनवरी | फरवरी | मार्च | अप्रैल | मई | जून | जुलाई | अगस्त | सितंबर | अक्टूबर | नवंबर | दिसंबर |
| कोड | 0 | 3 | 3 | 6 | 1 | 4 | 6 | 2 | 5 | 0 | 3 | 5 |
Note: लीप वर्ष होने पर :-
- जनवरी के लिए –6
- फ़रवरी के लिए –2 लिया जाता है
विषम दिन तथा दिन (Odd Day and Day)
| दिन का नाम | रविवार | सोमवार | मंगलवार | बुधवार | गुरुवार | शुक्रवार | शनिवार |
विषम दिन | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
प्रश्नों के प्रकार (Type of Questions)
Type-1 दिए गए Date का Day मालूम करना
Trick -1
विषम दिन(Odd day) = { वर्ष की संख्या + (वर्ष की संख्या/4) + महीने का कोड + तारीख / 7
Question – 12 जून 1987 को कौन सा दिन था
Solution –
वर्ष की संख्या – 87
महीने का कोड – 4
तारीख – 12
By trick – विषम दिन = { 87 +(87/4)+ 4 +12 } / 7
={87 + 21+4+ 12}/7
=124/7 =17 शेषफल 5
अतः विषम संख्या 5 है तो ऊपर दिन वार के कोड से शुक्रवार होगा
Note= इस तरह के प्रश्न हल करने में दो बातों का जरूर ध्यान रखें
- पहला जब वर्ष की संख्या में 4 का भाग देगे तो वहां पर भागफल लिखा जाएगा तथा शेषफल को छोड़ देगे
तथा जब विषम संख्या निकलते है पूरे समीकरण को 7 का जब भाग देगे तो वहां पर शेषफल लिखा जाएगा
इसप्रकार यदि आपने ऊपर दिए गई बातो को सही से याद कर लिए तो आपको प्रश्न हल करने में कोई परेशानी नहीं होगी
Trick -2 जब दो Complete date के बीच 1 वर्ष से कम का अंतर हो
- इसके लिए दोनों Date के बीच कुछ दिनों की संख्या ज्ञात करें
- दिनों की संख्या में 7 का भाग देने पर शेषफल ज्ञात करें
- Complete Date से Future के लिए शेषफल को दिए गए दिन में जोड़े तथा Past के लिए दिए गए दिन में से शेषफल को घटाकर दिन मालूम करें
Question – यदि 10 फरवरी 2003 को सोमवार था तो 17 जुलाई 2003 को कौन सा दिन होगा
Solution-
10 फरवरी से 17 जुलाई में कुल दिनों की संख्या
संख्या = फरवरी (28-10)+ मार्च (31) + अप्रैल (30)+ मई (31)+ जून (30) जुलाई(17)
=18+31+30+31+30+17=157
विषम दिन =157/7 =शेषफल=3
सोमवार +3= गुरुवार
Note: अगर आगे की दिन पूछ रहा है तो दिए गए दिन में शेषफल जोड़ा जाएगा अगर यह पीछे की दिन पूछता तो हम इसमें से घटा देते हैं
Type-3 Complete Date के आधार पर दिन ज्ञात करना अर्थात जब 2 वर्षों की तारीख और महीना समान दिया हो
Trick -3 विषम दिनों की संख्या = { (अंतिम वर्ष – पहला वर्ष ) + उनमे कुल लिप वर्ष } / 7
Question -3 यदि 1 जनवरी 1911 को बुधवार माना जाए तो 1 जनवरी 1971 को कौन सा दिन होगा
Solution-
विषम दिनों की संख्या = { (अंतिम वर्ष – पहला वर्ष ) + उनमे कुल लिप वर्ष } / 7
={ (1971- 1911) + 15} /7
= (60+ 15) / 7
= 75/7
= 10 भागफल ओर विषम दिन 5
विषम दिन 5=शुक्रवार ( ऊपर दिन तालिका से )
अतः 1 जनवरी 1911 को बुधवार है तो
बुधवार + 5 = सोमवार
Note: चूँकि रविबार में 3 जोड़ने से प्रश्न का दिन प्राप्त होता है अत: यंहा भी प्राप्त वास्तविक दिन में 3 जोड़कर ही दिन प्राप्त करेगें
Type -4 जब दिया गया वर्ष समान है तथा तारीख और महीना अलग है तो
Trick -4 ऐसे प्रश्नों को हल करते समय हम जो पहली तारीख दी हुई है उसको उस महीने के कुल दिनों में से घटा देते हैं तथा बाकी आगे के महीने के दिन और अंतिम महीने का दिन ऐसे ऐसे रख देते हैं
Question : 1 जनवरी 2000 को सोमवार हो तो 10 जुलाई 2000 को कौन सा दिन होगा
Solution–
1 जनवरी से 10 जुलाई के बीच कुल दिनों की संख्या = जनवरी (31-1)+ फरवरी(29)+ मार्च (31 )+ अप्रैल (30) + मई (31)+ जून (30) +जुलाई (10)
= 30 + 29 + 31+ 30 +31+30 +10
=191 / 7
= 27 भागफल 2 शेषफल
= सोमवार + 2= बुधवार
Note : उपरोक्त प्रश्न में फ़रवरी 29दिन का होगा क्योकि वर्ष 2000 लीप वर्ष है
अंतर समझे
1- अगस्त से फरवरी का अर्थ है
अगस्त-सितंबर अक्टूबर-नवंबर दिसंबर जनवरी-फरवरी
2 – फरवरी से अगस्त का अर्थ
फरवरी-मार्च – अप्रैल-मई-जून- जुलाई- अगस्त
Type -5 जब दिए गए 2 वर्षों की तारीख महीना और वर्ष तीनों ही भिन्न हो
Trick -5 इसके लिए हम वही अपनी कोड वाली विधि और ट्रिक यूज़ करेंगे लेकिन इसमें हमें दोनों का अलग-अलग विषम अंक निकालना पड़ेगा
विषम दिन = { वर्ष की संख्या +( वर्ष की संख्या / 4 )+ महीने का कोड + तारीख } / 7
Question: 10 अगस्त 1955 को गुरुवार था तो 22 अक्टूबर 1993 को कौन सा दिन होगा
Solution-
10 अगस्त 1955 के बीच कुल दिनों की
विषम दिन={ 55 +(55/4)+ 2 + 10} / 7
=(55+ 13 + 12) / 7
=80 / 7
= 11 भागफल 3 विषम दिन
3 मतलब बुधवार लेकिन प्रश्न में गुरुवार दिया है तो
बुधवार + 1 = गुरुवार
अब 22 अक्टूबर 1993 में के बीच कुल दिनों की
विषम दिन={ 93 +(93/4)+ 0 + 22 } / 7
=( 93+ 23 + 22) / 7
=138 / 7
= 19 भागफल 5 विषम दिन
अब हमने ऊपर दिन को सही करने के लिए 1 जोड़ा था बुधवार में तो यहां भी वही जोड़ देगे
= शुक्रवार + 1 = शनिवार
Trick-6 साधारण वर्ष का पहला दिन एवं अंतिम दिन दोनों समान होता है
लीप वर्ष का पहला दिन और अंतिम दिन में 1 दिन का अंतर होगा
Trick -7
- निम्न महीनों के प्रथम दिन समान होते हैं
- फरवरी-मार्च , नवंबर
- जनवरी , अक्टूबर
- अप्रैल, जुलाई
4. सितंबर, दिसंबर
- .निम्न महीनों के अंतिम दिन समान होते हैं
- जनवरी-फरवरी ,अक्टूबर
- मार्च, जून
- अप्रैल, दिसंबर
- अगस्त, नवंबर
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