Clock Aptitude

Clock problems in aptitude tests typically involve understanding the movement of the hour and minute hands and calculating the angles or time intervals between different positions. These problems require a good grasp of how the clock operates, including the speeds of the hands and their positions at different times.

1. At what time between 4 and 5 o'clock will the hands of a clock be at a right angle?

At 4 o'clock, the hour hand is at 4 and the minute hand is at 12. They are 20 minute spaces apart. To be at a right angle, the minute hand needs to be 15 minute spaces away from the hour hand. This will happen when the minute hand has moved 35 minute spaces from 12, which occurs at 4:21.

2. How many times in a day do the two hands of a clock coincide?

The hands of a clock coincide 11 times every 12 hours. Therefore, in a day (24 hours), they coincide 22 times.

3. At what time between 2 and 3 o'clock will the hands of a clock be together?

At 2 o'clock, the hour hand is at 2 and the minute hand is at 12. The minute hand needs to gain 10 minute spaces over the hour hand to be together. This happens in 10/11 of an hour, or approximately at 2:10.

4. If it is 8 o'clock now, how many degrees will the hour hand rotate to show 2 o'clock?

From 8 to 2, there are 6 hours. The hour hand rotates 30° per hour. So, it will rotate 6 × 30° = 180°.

5. At 3:40, what is the angle between the hour and minute hands of a clock?

At 3:40, the minute hand is at 8 and the hour hand is 2/3 of the way between 3 and 4. The angle between each number is 30°. So, the angle is 30° × (5 - 2/3) = 130°.

6. How many times in a day do the hands of a clock form a straight line?

The hands of a clock form a straight line 11 times every 12 hours, but at 6 o'clock, they form a straight line once instead of twice. Therefore, in a day, they form a straight line 11 × 2 - 1 = 25 times.

7. At what time exactly will the hands of a clock form an angle of 60°?

The hands of a clock form a 60° angle when they are 20 minutes apart. At 1:00, the hands are 5 minutes apart. The minute hand will need to move 15 minutes more than the hour hand, which happens at approximately 1:10.

8. If it is 10:00 now, after how many minutes will the hands of the clock be at right angles?

At 10:00, the hour hand is on 10 and the minute hand on 12. They will be at right angles when the minute hand is on 3 and the hour hand is 1/6 of the way between 10 and 11. This will be after 35 minutes.

9. At what time between 7 and 8 o'clock will the hands of a clock be in the opposite directions?

The hands are opposite when they are 30 minutes apart. At 7:00, they are 5 minutes apart. The minute hand will need to gain 25 more minutes, which happens at approximately 7:10.

10. If a clock shows 3:30, what is the angle between its hands?

At 3:30, the minute hand is on 6 and the hour hand is halfway between 3 and 4. The angle between each number is 30°. So, the angle is 30° × (3 - 1/2) = 75°.

11. How many times in a day does the minute hand of a clock overtake the hour hand?

The minute hand overtakes the hour hand 11 times every 12 hours. Therefore, in a day, it happens 22 times.

12. At 5:30, what is the angle between the hour and minute hands of a clock?

At 5:30, the minute hand is on 6 and the hour hand is halfway between 5 and 6. The angle between each number is 30°. So, the angle is 30° × 1/2 = 15°.

13. What is the angle between the hour and minute hands of a clock when the time is 2:20?

At 2:20, the hour hand is 1/3 of the way between 2 and 3, and the minute hand is on 4. The angle between each number is 30°. So, the angle is 30° × (2 + 1/3 - 4) = 50°.

14. At what time between 9 and 10 o'clock will the hands of a clock be together?

The hands are together when the minute hand is 45 minute spaces ahead of the hour hand. At 9:00, the hands are 45 minute spaces apart. The minute hand will catch up in 45/55 of an hour, which is approximately at 9:25.

15. At 4:20, what is the angle between the hour and minute hands of a clock?

At 4:20, the minute hand is on 4 and the hour hand is 1/3 of the way between 4 and 5. The angle between each number is 30°. So, the angle is 30° × (1/3) = 10°.

16. How many times between 12 noon and 12 midnight do the hour and minute hands of a clock form an angle of 180°?

The hands of a clock form an angle of 180° 11 times in every 12-hour period. Therefore, between 12 noon and 12 midnight, it happens 11 times.

17. At what time between 1 and 2 o'clock will the hands of a clock be at an angle of 90°?

The hands of a clock are at 90° when the minute hand is 15 minute spaces away from the hour hand. At 1:00, the hour hand is at 5 past. It needs to be at either 20 past or 50 past for the angle to be 90°. Since we are looking between 1 and 2 o'clock, the time will be approximately 1:25.

18. If a clock shows 6:15, what is the angle between its hands?

At 6:15, the minute hand is at 3 and the hour hand is at 6. The hour hand has also moved a quarter of the way to the next hour mark. The angle between each number is 30°. So, the angle is 30° × (3 - 0.25) = 77.5°.

19. At what time between 10 and 11 o'clock will the hands of a clock be in a straight line but not together?

The hands are in a straight line but not together when they are 30 minutes apart. This occurs when the minute hand is 15 minutes ahead or behind the hour hand. At 10 o'clock, the hands are 10 minutes apart. The minute hand needs to gain 20 minutes or lose 40 minutes. The gain of 20 minutes occurs approximately at 10:27.

20. At 8:40, what is the angle between the hour and minute hands of a clock?

At 8:40, the minute hand is at 8 and the hour hand is 2/3 of the way between 8 and 9. The angle between each number is 30°. So, the angle is 30° × (2/3) = 20°. Since both hands are on the same side of the clock, the angle between them is 180° - 20° = 160°.