Clock problems
- 1. The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
Options- A. 0°
- B. 10°
- C. 5°
- D. 20° Discuss
Correct Answer: 10°
Explanation:
| Angle traced by hour hand in | 13 | hrs = | ❨ | 360 | x | 13 | ❩ | ° | = 130°. |
| 3 | 12 | 3 |
| Angle traced by min. hand in 20 min. = | ❨ | 360 | x 20 | ❩ | ° | = 120°. |
| 60 |
∴ Required angle = (130 - 120)° = 10°.
- 2. At what angle the hands of a clock are inclined at 15 minutes past 5?
Options- A.
58 1 ° 2 - B. 64°
- C.
67 1 ° 2 - D.
72 1 ° 2
Discuss
Correct Answer:
| 67 | 1 | ° |
| 2 |
Explanation:
| Angle traced by hour hand in | 21 | hrs = | ❨ | 360 | x | 21 | ❩ | ° | = | 157 | 1 | ° |
| 4 | 12 | 4 | 2 |
| Angle traced by min. hand in 15 min. = | ❨ | 360 | x 15 | ❩ | ° | = 90°. |
| 60 |
| ∴ Required angle = | ❨ | 157 | 1 | ❩ | ° | - 90° = 67 | 1 | ° |
| 2 | 2 |
- 3. A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:
Options- A.
59 7 min. past 3 12 - B. 4 p.m.
- C.
58 7 min. past 3 11 - D.
2 3 min. past 4 11
Discuss
Correct Answer: 4 p.m.
Explanation:
| Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min. = | 37 | hrs. |
| 4 |
3 min. 5 sec. of this clock = 3 min. of the correct clock.
| ⟹ | 37 | hrs of this clock = | 1 | hrs of the correct clock. |
| 720 | 20 |
| ⟹ | 37 | hrs of this clock = | ❨ | 1 | x | 720 | x | 37 | ❩ | hrs of the correct clock. |
| 4 | 20 | 37 | 4 |
= 9 hrs of the correct clock.
∴ The correct time is 9 hrs after 7 a.m. i.e., 4 p.m.
- 4. How many times in a day, the hands of a clock are straight?
Options- A. 22
- B. 24
- C. 44
- D. 48 Discuss
Correct Answer: 44
Explanation:
∴ In 24 hours, the hands coincide or are in opposite direction 44 times a day.
- 5. At what time between 4 and 5 o'clock will the hands of a watch point in opposite directions?
Options- A. 45 min. past 4
- B. 40 min. past 4
- C.
50 4 min. past 4 11 - D.
54 6 min. past 4 11
Discuss
Correct Answer:
| 54 | 6 | min. past 4 |
| 11 |
Explanation:
To be in opposite directions, they must be 30 min. spaces apart.
∴ Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min.
| 50 min. spaces are gained in | ❨ | 60 | x 50 | ❩min. or 54 | 6 | min. |
| 55 | 11 |
| ∴ Required time = 54 | 6 | min. past 4. |
| 11 |
- 6. At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but, not together?
Options- A. 5 min. past 7
- B.
5 2 min. past 7 11 - C.
5 3 min. past 7 11 - D.
5 5 min. past 7 11
Discuss
Correct Answer:
| 5 | 5 | min. past 7 |
| 11 |
Explanation:
At 7 o'clock, they are 25 min. spaces apart.
∴ Minute hand will have to gain only 5 min. spaces.
55 min. spaces are gained in 60 min.
| 5 min. spaces are gained in | ❨ | 60 | x 5 | ❩min | = 5 | 5 | min. |
| 55 | 11 |
| ∴ Required time = 5 | 5 | min. past 7. |
| 11 |
- 7. How many times are the hands of a clock at right angle in a day?
Options- A. 22
- B. 24
- C. 44
- D. 48 Discuss
Correct Answer: 44
Explanation:
∴ In 24 hours, they are at right angles 44 times.
- 8. At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
Options- A.
5 1 " 11 - B.
12 4 " 11 - C.
13 4 " 11 - D.
16 4 " 11
Discuss
Correct Answer:
| 16 | 4 | " |
| 11 |
Explanation:
To be coincident, it must gain 15 min. spaces.
55 min. are gained in 60 min.
| 15 min. are gained in | ❨ | 60 | x 15 | ❩min | = | 16 | 4 | min. |
| 55 | 11 |
| ∴ The hands are coincident at 16 | 4 | min. past 3. |
| 11 |
- 9. The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:
Options- A. 80°
- B. 75°
- C. 60°
- D. 105° Discuss
Correct Answer: 75°
Explanation:
| Angle traced by hour hand in | 17 | hrs = | ❨ | 360 | x | 17 | ❩ | ° | = 255°. |
| 2 | 12 | 2 |
| Angle traced by min. hand in 30 min. = | ❨ | 360 | x 30 | ❩ | ° | = 180°. |
| 60 |
∴ Required angle = (255 - 180)° = 75°.
- 10. How many times do the hands of a clock coincide in a day?
Options- A. 20
- B. 21
- C. 22
- D. 24 Discuss
Correct Answer: 22
Explanation:
AM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
PM
12:00
1:05
2:11
3:16
4:22
5:27
6:33
7:38
8:44
9:49
10:55
The hands overlap about every 65 minutes, not every 60 minutes.
∴ The hands coincide 22 times in a day.
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