__Question:__How many times do the hands of a clock coincide in a day?

**Options:**

A. | 20 | |

B. | 21 | |

C. | 22 | |

D. | 24 |

**Answer: Option C**

The 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.

So, The hands coincide 22 times in a day.

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## More Questions on This Topic :

__Question 1.__At what time, in minutes, between 3 oclock and 4 oclock, both the needles will coincide each other?

**Options:**

- \(5\frac{1}{11}\)
- \(12\frac{4}{11}\)
- \(13\frac{4}{11}\)
- \(16\frac{4}{11}\)

**Answer: Option D**

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 \(\left(\frac{60}{55}\times15\right)min. = 16\frac{4}{11}min.\)

So, The hands are coincident at \(16\frac{4}{11}min. past 3\)

**Options:**

- 45 min. past 9
- 50 min. past 9
- \(49\frac{1}{11} min. past 9\)
- \(48\frac{2}{11} min. past 9\)

**Answer: Option C**

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 \(\left(\frac{60}{55}\times45\right)min. or 49\frac{1}{11}min.\)

So, The hands are together at \(49\frac{1}{11} min. past 9\)

__Question 3.__At what time between 4 and 5 oclock will the hands of a watch point in opposite directions?

**Options:**

- 45 min. past 4
- 40 min. past 4
- \(50\frac{4}{11} min. past 4\)
- \(54\frac{6}{11} min. past 4\)

**Answer: Option D**

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.

So, Minute hand will have to gain 50 min. spaces.

55 min. spaces are gained in 60 min.

50 min. spaces are gained in \(\left(\frac{60}{55}\times50\right)min. or 54\frac{6}{11}min. \)

So, Required time = \(54\frac{6}{11} min. past 4\)

__Question 5.__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:**

- 2 p.m. on Tuesday
- 2 p.m. on Wednesday
- 3 p.m. on Thursday
- 1 p.m. on Friday

**Answer: Option B**

Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.

So, The watch gains \(\left(2+4\frac{4}{5}\right)min. or \frac{34}{5}min. in 170 hrs\)

Now, \(\frac{34}{5}\) min. are gained in 170 hrs.

So, 2 min. are gained in \(\left(170\times\frac{5}{34}\times2\right)hrs= 50 hrs.\)

So,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.

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