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- Question
How many times do the hands of a clock coincide in a day?
Options- A. 20
- B. 21
- C. 22
- D. 24
- Correct Answer
- 22
ExplanationThe hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).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.
Clock problems
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- 1. 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°.
- 2. 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:
At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.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 - 3. 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 12 hours, they are at right angles 22 times.∴ In 24 hours, they are at right angles 44 times.
- 4. 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:
When the hands of the clock are in the same straight line but not together, they are 30 minute spaces apart.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 - 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:
At 4 o'clock, the hands of the watch are 20 min. spaces apart.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. 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.
- 7. 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 - 8. 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 - 9. 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 - 10. 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
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