Calendars and Clock

Basic Structure of a Calendar

1. Ordinary year: Any year which 365 days is called an ordinary year. Ex: 1879, 2009, 2019, etc.
2. Leap year: Any year which has 366 days is called a leap year. Ex: 2012, 2016 2020 etc. (if the year is divisible by 4, it is called leap year)
3. The division of the number 365 by 7 gives the quotient 52 and remainder 1 which indicates that an ordinary year has 52 weeks and one extra day. This extra day is referred to as an “odd day” throughout the calendar topic.
4. A leap year has 366 days, the division of the number 366 by 7 gives the quotient 52 and remainder 2. This indicates that a leap year has 52 weeks and 2 extra days. These two extra days are also referred to as “odd days”.
5. An ordinary year has one odd day, whereas a leap year has two odd days.

Concept of an Odd Day

Number of odd days in a month

• January has 31 days, irrespective of whether it’s an ordinary year or leap year. The division of the number 31 by 7 provides the remainder 3 hence January has 3 odd days. On generalising, any month which has 31 days has 3 odd days and any month which has 30 days has 2 odd days.
• The only exception happens in the case of February. The February month of an ordinary year has 28 days, division of 28 by 7 provides zero as remainder. Hence, the number of odd days in February of an ordinary year will have 0 odd days and that of leap years will have 1 odd day as February in a leap year has 29 days.
• Refer to the following three tables for odd days:

Table 1

Table 2

Table 3

Clock theory

In every hour

1. Both the Hands coincide once. At this point the angle between them is 0°.
2. The hands are straight (point in opposite directions) once. At this point the angles between them are 180°.
3. The hands are twice perpendicular to each other. At this point the angle between them is 90°.
4. (a) In 60 min the minute hand covers 360°.

5. When the two hands are at right angles, they are 15min spaces apart.
6. When the two hands are in opposite directions, they are 30 min spaces apart.
7. In 60 min the minute hand gains 55 min on the hour hand.
8. The minute hand moves 12 times as fast as the hour hand.
9. Too Fast: If a clock indicates 7 : 15, when the correct time is 7, it is said to be 15 min too fast.
10. Too Slow: If a clock indicates 7 : 30, when the correct time is 7: 45 , it is said to be 15 min too slow.

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Practice Questions

1. January 3, 2007 was Wednesday. What day of the week fell on January 3, 2008?
a. Tuesday
b. Friday
c. Thursday
d. Saturday

2. If the third day of a month is Monday, then which day of the week will be the fifth day from the 21st of that month?
a. Tuesday
b. Monday
c. Wednesday
d. Thursday

3. If 5th January 1991 was a Saturday, what day of the week was 4th March 1992?
a. Monday
b. Wednesday
c. Friday
d. Saturday

4. 4th April, 1988 was Monday. What day of the week was it, on 6th November 1987?
a. Tuesday
b. Friday
c. Sunday
d. Saturday

5. Find the day of the week on 26th January 1950.
a. Tuesday
b. Friday
c. Wednesday
d. Thursday

6. Find the day of the week on 15th August 1947.
a. Tuesday
b. Wednesday
c. Friday
d. Thursday

7. Find the day of the week on 16th December, 1971.
a. Tuesday
b. Sunday
c. Thursday
d. Friday

8. In a month of 31 days, the third Thursday falls on the 16th. What will be the last day of the month?
a. 5th Friday
b. 4th Saturday
c. 5th Wednesday
b. 5th Thursday

9. What were the days of the week on 17th August, 2010?
a. Sunday
b. Wednesday
c. Tuesday
b. Friday

10. If a month in a year starts with Monday, then the date of the fourth day after the second Saturday in that month, will be? (UPSC 2019)
a. 16
b. 17
c. 18
d. 19

11. From January 1, 2021, the price of petrol (in Rupees per litre) on mth day of the year is 80 + 0.1 m, where m = 1, 2, 3, ..., 100 and thereafter remains constant. On the other hand, the price of diesel (in Rupees per litre) on the nth day of 2021 is 69 + 0.15 n for any n. On which date in the year 2021 are the prices of these two fuels equal? (UPSC 2021)
a. 21st May
b. 20th May
c. 19th May
d. 18th May

12. Find the angle between the hour hand and the minute hand of a clock when the time is 5 : 35 pm.
a. 42.5 degrees
b. 167.5 degrees
c. 168 degrees
d. 49 degrees

13. Seeta and Geeta go for a swim after a gap of every 2 days and every 3 days respectively. If on 1st January both of them went for a swim together, when will they go together next?
(UPSC 2019)
a. 7th January
b. 8th January
c. 12th January
d. 13th January

14. If the 3rd day of a month is Monday, which of the following will be the fifth day from 21st of the month? (UPSC 2014)
a. Monday
b. Tuesday
c. Wednesday
d. Thursday

15. Which year has the same calendar as that of 2009? (UPSC 2019)
a. 2018
b. 2017
c. 2016
d. 2015

16. If in the particular year 12th January is a Sunday, then which one of the following is correct?
(UPSC 2020)
a) 15th July is a Sunday if the year is a leap year.
b) 15th July is a Sunday if the year is not a leap year.
c) 12th July is Sunday if the year is a leap year.
d) 12th July is a not Sunday if the year is a leap year

17. If second and fourth Saturdays and all Sundays are taken as only holidays for an office, what would be the minimum number of possible working days of any month of any year? (UPSC 2017)
a. 23
b. 22
c. 21
d. 20

18. Which day is 10th October, 2027?
a. Sunday
b. Monday
c. Tuesday
d. Saturday

19. Which date of June 2099 among the following is Sunday? (UPSC 2022)
a. 4
b. 5
c. 6
d. 7

20. A watch which gains uniformly, is 5 min slow at 7 o'clock in the morning on Sunday and it is 5 min 48 s fast at 7 pm on following Sunday. Which day was it correct?
a. Friday
b. Saturday
c. Tuesday
d. Wednesday

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