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Clock – Aptitude Questions and Answers

Last Updated : 06 Nov, 2024
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Clock questions are commonly included in quantitative aptitude exams. These questions typically require the application of basic arithmetic and algebraic concepts to solve problems related to time and time difference between two events.

Prerequisites: Clock – Fundamentals

Aptitude Questions on Clocks

Q1: Find the angle between the hands of a clock at 3:20 PM. 

Solution

At 3:00 PM, the angle made by the minute hand = 0 degree, and the angle made by the hour hand = 3 x angle made by the hour hand in one hour = 3 x 30 = 90 degrees Now, in the next 20 minutes, angle made by the minute hand = 20 x angle made by the minute hand in 1 minute = 20 x 6 = 120 degrees and angle made by the hour hand = 20 x angle made by the hour hand in 1 minute = 20 x 0.50 = 10 degrees => Angle made by the minute hand at 3:20 PM = 0 + 120 = 120 degrees => Angle made by the hour hand at 3:20 PM = 90 + 10 = 100 degrees Therefore, the angle between the hands of the clock at 3:20 PM = 120 – 100 = 20 degrees.

Another Method: At 3:00 PM, the angle made by the minute hand = 0 degree, and the angle made by the hour hand = 3 x angle made by the hour hand in one hour = 3 x 30 = 90 degrees => Initial angle between the two hands = 90 degrees Now, we know that the difference between the two hands of the clock increases every minute by 5.50 degrees. => Difference between the hands of the clock after 20 minutes = 20 x 5.50 = 110 degrees Therefore, the difference between the two hands at 3:20 PM = 110 – 90 = 20 degrees.

Q2: At what time between 3 PM and 4 PM would the two hands of the clock be together? 

Solution

At 3 PM, the hour hand would be at 15 spaces and the minute hand would be at 0 spaces. The minute hand would have to cover these extra 15 spaces in order to meet the hour hand. Now, 55 minutes are gained by the minute hand in 60 minutes. => 15 minutes would be gained in (60 / 55) x 15 = 180 / 11 minutes Thus, the two hands of the clock meet at 180 / 11 minutes past 3 PM, i.e., around 3:16:22 PM.   

Q3: How many times in a day the two hands of a clock coincide? 

Solution

Between 11 to 1, the hands of the clock coincide only once, i.e., at 12. At 12:00 AM and 12:00 PM, the hour hand and the minute hand do not coincide with each other So, every 12 hours, they coincide 11 times. Therefore, the two hands of the clock coincide 22 times in a day.   

Q4: At what time between 5 and 6 o’clock, do the minute and hour hands make an angle of 34 degree with each other

Solution

The angle between the minute hand and the hour hand at 5 o’clock is 150 degrees.
The angle between the hands becomes 34 degrees when the angle changes by 116 degrees and 184 degrees, i.e. (150-34) and (150+34).
The angle changes by 5.5 degrees in 1 min.
The angle changes by 116 degrees in 1/5.5 x 116=21 1/11 min.
The angle changes by 184 degrees in 1/5.5 x 184=33 5/11 min.
Therefore the angle between the two hands is 34 degrees when the time is 5 hr 21 1/11 min, and again at 5 hr 33 5/11 min. 

Practice Questions on Clock

1. At what time between 3 and 4 o’clock will the hands of a clock be at right angles?

2. At what time between 5 and 6 will the hands of a clock be in opposite directions?

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

4. At what time between 4 and 5 o’clock will the minute hand be 10 minute spaces ahead of the hour hand?

5. How many degrees does the hour hand of a clock turn through between 6:20 and 8:40?

6. A clock shows 6:45. What is the angle between the hour and minute hands?

7. A clock is set correctly at 5:00 AM. The clock gains 3 minutes in 1 hour. What will be the true time when the clock indicates 10:00 PM of the same day?

8. The minute hand of a clock overtakes the hour hand at intervals of 65 minutes of correct time. How much does the clock gain or lose in a day?

9. A clock strikes once at 1 o’clock, twice at 2 o’clock, thrice at 3 o’clock and so on. How many times will it strike in 24 hours?

10. A watch which gains uniformly is 2 minutes slow at noon on Monday and is 4 minutes fast at 6 PM on the following Monday. When was it correct?


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