Clock and Calendar Notes for SSC Exams

Clock and calendar questions test your knowledge of time. In the clock part, you find the angle between the hands or the time when the hands meet. In the calendar part, you find the day of a given date using odd days. These clock and calendar notes for SSC explain every formula with solved examples and practice questions in simple language.

Clock: Basic Facts

Angle Between the Hands

Angle = |30H − 5.5M|, where H is the hour and M is the minutes. If the answer is more than 180 degrees, subtract it from 360.

Example 1. Find the angle at 3:30.
|30 × 3 − 5.5 × 30| = |90 − 165| = 75 degrees.

Example 2. Find the angle at 9:15.
|270 − 82.5| = 187.5, so the angle is 360 − 187.5 = 172.5 degrees.

Important Facts About the Hands

• The two hands overlap after every 65 5/11 minutes in a correct clock.
• If a clock overlaps in a time other than 65 5/11 minutes, it is slow or fast.
• At 12 o'clock the hands overlap, and at 6 o'clock they are in a straight line opposite to each other.

Mirror Image of a Clock

The mirror image of a clock time is found by subtracting the time from 11:60. For example, the mirror image of 4:20 is 11:60 − 4:20 = 7:40.

Calendar: Odd Days

Odd days are the extra days left after taking out the full weeks (the remainder when the number of days is divided by 7).

Leap Year Rules

• A year divisible by 4 is a leap year, such as 2024 and 2028.
• A century year (like 1900 or 2100) is a leap year only if it is divisible by 400. So 2000 is a leap year, but 1900 is not.
• February has 29 days in a leap year and 28 days in an ordinary year.

Odd Days of the Months

Day Code

Solved Examples

Example 3. If today is Wednesday, what will be the day after 100 days?
100 divided by 7 leaves 2, so the day is Wednesday + 2 = Friday.

Example 4. If 1 January 2001 was Monday, which day was 1 January 2002?
2001 is an ordinary year with 1 odd day, so 1 January 2002 was Tuesday.

Example 5. Independence Day (15 August 1947) fell on which day?
It was a Friday. This and 26 January 1950 (Thursday) are well-known dates for such questions.

Quick Tips

• For clock angles, use |30H − 5.5M| and always check if the angle is above 180.
• Remember the odd days table: 100 years = 5, 200 = 3, 300 = 1 and 400 = 0.
• For day problems, count odd days and add them to the known day.
• Check the leap year rule for century years before you solve.

Quick Revision Points

• Minute hand moves 6 degrees per minute and hour hand 0.5 degree per minute.
• Angle = |30H − 5.5M|.
• Hands overlap 11 times in 12 hours.
• Ordinary year has 1 odd day and leap year has 2 odd days.
• Mirror image time = 11:60 − the given time.

Practice Questions With Answers

1. Find the angle between the hands at 3:00.
   Answer: 90 degrees
2. Find the angle between the hands at 6:00.
   Answer: 180 degrees
3. How many times do the hands of a clock overlap in 12 hours?
   Answer: 11
4. Find the angle at 2:30.
   Answer: 105 degrees (|60 − 165|)
5. How many odd days are there in 400 years?
   Answer: 0
6. Is 2100 a leap year?
   Answer: No
7. How many odd days are there in an ordinary year?
   Answer: 1
8. If today is Monday, what will be the day after 50 days?
   Answer: Tuesday (50 mod 7 = 1)
9. Find the mirror image time of 3:40.
   Answer: 8:20
10. If 1 January 2023 was Sunday, which day was 1 January 2024?
    Answer: Monday

How to Practise This Chapter

Practise five clock and five calendar questions daily and learn the odd days table by heart. Then attempt timed sets from our practice papers and the previous year papers page. Read the previous chapter, Syllogism, and see all topics on the Reasoning notes page. For the maths basics of time, also read the Quantitative Aptitude notes.

Frequently Asked Questions

What is the formula for the angle between the hands of a clock?

The angle is the absolute value of 30 times the hour minus 5.5 times the minutes.

How many degrees does the minute hand move in one minute?

The minute hand moves 6 degrees in one minute.

How many degrees does the hour hand move in one minute?

The hour hand moves half a degree in one minute.

How many times do the hands of a clock overlap in a day?

The hands overlap 22 times in a day (24 hours).

How many times are the hands at right angles in a day?

The hands are at right angles 44 times in a day.

What are odd days?

Odd days are the extra days left after removing the complete weeks from a number of days.

How many odd days are there in a leap year?

A leap year has 366 days, so it has 2 odd days.

How do I check a leap year?

A year divisible by 4 is a leap year, but a century year must be divisible by 400.

How do I find the mirror image of a clock time?

Subtract the given time from 11:60 to get the mirror image time.

How can I find the day for any date?

Count the odd days from a known date and add them to the known day.

How many questions come from clock and calendar in SSC exams?

Usually one or two questions come from clock and calendar in SSC Reasoning papers, but the number changes from year to year.

Is the clock chapter difficult?

No. It becomes easy if you remember the angle formula and the speeds of the two hands.