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Clocks and Calendars
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Clocks and Calendars
Clocks and Calendars are common topics in quantitative aptitude sections of many placement tests and competitive exams. These topics test a candidate’s ability to apply logical thinking, numerical skills, and time-based calculations.
Below are the key concepts and problem-solving techniques related to clocks and calendars.
Clocks
Analogue Clock
An analogue clock consists of:
-
An hour hand
-
A minute hand
-
Sometimes a second hand
Important facts:
-
In 12 hours, the hour hand completes one full revolution.
-
In 60 minutes, the minute hand completes one full revolution.
-
In 60 seconds, the second hand completes one full revolution.
Time and Angle Calculations
Formulas:
-
Angle covered by the hour hand
= (30 × hours) + (0.5 × minutes) -
Angle covered by the minute hand
= (6 × minutes) -
Angle between the hour and minute hands
= |Hour hand angle − Minute hand angle|
Clock problems usually involve:
-
Finding angles between hands
-
Determining time intervals
-
Finding when hands coincide or form a specific angle
Example 1
Find the angle between the hour and minute hands at 3:20.
Solution:
-
Hour hand angle = (30 × 3) + (0.5 × 20)
= 90 + 10
= 100° -
Minute hand angle = 6 × 20
= 120° -
Angle between hands
= |100 − 120|
= 20°
Example 2
At what time between 3 and 4 o’clock will the hour and minute hands coincide?
Solution (concept):
The minute hand moves faster than the hour hand and catches up once every hour.
The hands coincide approximately every 65 minutes.
After 3:00, they coincide at about:
3:16:22 (approximately)
Calendars
Leap Year Rules
A year is a leap year if:
-
It is divisible by 4,
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Except years divisible by 100,
-
Unless they are also divisible by 400.
Example:
-
2000 → Leap year
-
1900 → Not a leap year
Finding the Day of a Given Date
You can determine the day of the week using methods such as:
-
Odd Days method
-
Doomsday algorithm
-
Zeller’s Congruence
Counting Days Between Two Dates
Steps:
-
Count the total years between the dates.
-
Add the number of leap years.
-
Count the days in the months between the dates.
-
Add the remaining days in the final month.
Example 1
What day of the week was January 1, 2022?
Answer:
January 1, 2022, was a Saturday.
Example 2
How many odd days are there in 600 years?
Solution concept:
-
400 years = 0 odd days (complete cycle)
-
Remaining years = 600 − 400 = 200 years
Odd days in 200 years:
-
200 × 1 = 200 days
-
Leap year extra days ≈ 49
Total = 249 days
249 ÷ 7 → remainder 4
So, there are 4 odd days in 600 years.
Tips for Solving Clock and Calendar Problems
-
Read the question carefully.
-
Visualise the clock or date sequence if needed.
-
Identify what is being asked.
-
Apply the correct formula or rule.
-
Practise different types of questions to improve speed and accuracy.
