Clock problems
- 1. A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?
Options- A. 2 p.m. on Tuesday
- B. 2 p.m. on Wednesday
- C. 3 p.m. on Thursday
- D. 1 p.m. on Friday Discuss
Correct Answer: 2 p.m. on Wednesday
Explanation:
Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.
| ∴ The watch gains | ❨ | 2 + 4 | 4 | ❩min. | or | 34 | min. in 170 hrs. |
| 5 | 5 |
| Now, | 34 | min. are gained in 170 hrs. |
| 5 |
| ∴ 2 min. are gained in | ❨ | 170 x | 5 | x 2 | ❩hrs | = 50 hrs. |
| 34 |
∴ Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e., it will be correct at 2 p.m. on Wednesday.
- 2. An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon?
Options- A. 144°
- B. 150°
- C. 168°
- D. 180° Discuss
Correct Answer: 180°
Explanation:
| Angle traced by the hour hand in 6 hours = | ❨ | 360 | x 6 | ❩ | ° | = 180°. |
| 12 |
- 3. At what time between 5.30 and 6 will the hands of a clock be at right angles?
Options- A.
43 5 min. past 5 11 - B.
43 7 min. past 5 11 - C. 40 min. past 5
- D. 45 min. past 5 Discuss
Correct Answer:
| 43 | 7 | min. past 5 |
| 11 |
Explanation:
At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min.
| 40 min. spaces are gained in | ❨ | 60 | x 40 | ❩min | = | 43 | 7 | min. |
| 55 | 11 |
| ∴ Required time = 43 | 7 | min. past 5. |
| 11 |
- 4. The reflex angle between the hands of a clock at 10.25 is:
Options- A. 180°
- B.
192 1 ° 2 - C. 195°
- D.
197 1 ° 2
Discuss
Correct Answer:
| 197 | 1 | ° |
| 2 |
Explanation:
| Angle traced by hour hand in | 125 | hrs = | ❨ | 360 | x | 125 | ❩ | ° | = 312 | 1 | ° | . |
| 12 | 12 | 12 | 2 |
| Angle traced by minute hand in 25 min = | ❨ | 360 | x 25 | ❩ | ° | = 150°. |
| 60 |
| ∴ Reflex angle = 360° - | ❨ | 312 | 1 | - 150 | ❩ | ° | = 360° - 162 | 1 | ° | = 197 | 1° | . |
| 2 | 2 | 2 |
- 5. A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:
Options- A. 145°
- B. 150°
- C. 155°
- D. 160° Discuss
Correct Answer: 155°
Explanation:
Angle traced by hour hand in 12 hrs = 360°.
| Angle traced by hour hand in 5 hrs 10 min. i.e., | 31 | hrs = | ❨ | 360 | x | 31 | ❩ | ° | = 155°. |
| 6 | 12 | 6 |
- 6. At 3:40, the hour hand and the minute hand of a clock form an angle of:
Options- A. 120°
- B. 125°
- C. 130°
- D. 135° Discuss
Correct Answer: 130°
Explanation:
Angle traced by hour hand in 12 hrs. = 360°.
| Angle traced by it in | 11 | hrs = | ❨ | 360 | x | 11 | ❩ | ° | = 110°. |
| 3 | 12 | 3 |
Angle traced by minute hand in 60 min. = 360°.
| Angle traced by it in 40 min. = | ❨ | 360 | x 40 | ❩ | ° | = 240°. |
| 60 |
∴ Required angle (240 - 110)° = 130°.
- 7. At what time between 9 and 10 o'clock will the hands of a watch be together?
Options- A. 45 min. past 9
- B. 50 min. past 9
- C.
49 1 min. past 9 11 - D.
48 2 min. past 9 11
Discuss
Correct Answer:
| 49 | 1 | min. past 9 |
| 11 |
Explanation:
To be together between 9 and 10 o'clock, the minute hand has to gain 45 min. spaces.
55 min. spaces gained in 60 min.
| 45 min. spaces are gained in | ❨ | 60 | x 45 | ❩min or 49 | 1 | min. |
| 55 | 11 |
| ∴ The hands are together at 49 | 1 | min. past 9. |
| 11 |
- 8. How much does a watch lose per day, if its hands coincide every 64 minutes?
Options- A.
32 8 min. 11 - B.
36 5 min. 11 - C. 90 min.
- D. 96 min. Discuss
Correct Answer:
| 32 | 8 | min. |
| 11 |
Explanation:
55 min. spaces are covered in 60 min.
| 60 min. spaces are covered in | ❨ | 60 | x 60 | ❩min. | = 65 | 5 | min. |
| 55 | 11 |
| Loss in 64 min. = | ❨ | 65 | 5 | - 64 | ❩ | = | 16 | min. |
| 11 | 11 |
| Loss in 24 hrs = | ❨ | 16 | x | 1 | x 24 x 60 | ❩min. | = | 32 | 8 | min. |
| 11 | 64 | 11 |
- 9. How many times in a day, are the hands of a clock in straight line but opposite in direction?
Options- A. 20
- B. 22
- C. 24
- D. 48 Discuss
Correct Answer: 22
Explanation:
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).
So, in a day, the hands point in the opposite directions 22 times.
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