1. Find the angle between the hour hand and the minute hand of a clock when the time is 10:32.

(a) 316°

(b) 124°

(c) 192°

(d)

**Answer: (b)**

**Explanation:**

Angle traced by hour hand in 12 h = 360°

Angle traced by the hour hand in 10 hour 32 minutes =

Angle traced by minute in 60 min = 360°

Angle traced by the minute hand in 32 min

Required angle = (316°-192°) = 124°

2. An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 5 o’clock in the afternoon?

(a) 144°

(b) 150°

(c) 180°

(d) 270°

**Answer: (d)**

**Explanation:**

Angle traced by the hour hand in 9 hours.

3. The minute and the hour hand of a watch meet every 50 minutes. How much does the watch lose or gain time?

(a)

(b)

(c)

(d)

**Answer: (c)**

**Explanation:**

55 mins are gained by minute hand in 60 min.

But the hands of the clock in question coincide every 50 min.

4. The minute and the hour hand of a watch meet every 63 minutes. How much does the watch lose or gain time.

(a)

(b)

(c)

(d)

**Answer: (d)**

**Explanation:**

55 min are gained by minute hand in 60 min.

Thus, the hands of a correct clock in question coincide every 63 min.

5. At what time between 6 and 7’o clock will the hands of a clock be at right angle?

(a)

(b)

(c)

(d) none of these

**Answer: (a)**

**Explanation:**

At 6’o clock the minute hand will be 30 min spaces behind the hour hand. Now, when the two hands are at right angle, they are 15 min spaces apart. So, there are two cases.

Case i: when the minute hand is 15 min spaces behind the hour hand.

To be in this position, the minute hand will have to gain (30-15)=15 min spaces.

Now, 55 min spaces are gained in 60 min

Case ii: when the minute hand is 15 min spaces ahead of the hour hand.

To be in this position, the minute hand will have to gain 30+15 = 45 min spaces.

Now, 55 min spaces are gained in 60 min

6. At what time between 8 and 9 are the hands of a clock 7 min apart?

(a)

(b)

(c)

(d)

**Answer: (a)**

**Explanation:**

At 8’o clock, the minute hand is 40 min spaces behind the hour hand

Case I: minute hand is 7 min spaces behind the hour hand,

In this case, the minute hand has to gain (40-7) =33 minute spaces.

55 min are gained in 60 min

The hands will be 7 min apart at 36 min. past 8

Case II: minute hand is 7 min spaces ahead of the hour hand,

In this case, the minute hand has to gain

(40+7)=47 min spaces

55 min are gained in 60 mins

7. A watch gains time uniformly it was observed that it was 5 min slow at 1’o clock on Monday night on Friday at 7 p. m. it was 5 min 48 sec fast. When was it correct?

(a) 2.30 am on Tuesday

(b) 4.46 am on Wednesday

(c) 2.30 pm on Tuesday

(d) 4.52 pm on Wednesday

**Answer: (b)**

**Explanation:**

Time from 1 am on Monday to 7 pm on following Friday= 4 days 18 hrs

= 96 hrs + 18 hr = 114 hrs

8. A man goes out between 5. p. m and 6 p. m. when he comes back between 6 p. m. and 7 p. m. he observes that the two hands of a clock have interchanged their positions. Find out the man went out.

(a)

(b)

(c)

(d)

**Answer: (d)**

**Explanation:**

Let the man go out at a min past H.

Then, using the formula,

Now, H = 5 p.m.

9. A clock strikes 10 taking 18 seconds. In order to strike 14 at the same rates, the time taken is.

(a) 26 s

(b) 62 s

(c) 32 s

(d) none of these

**Answer: (a)**

**Explanation:**

There are 9 intervals when the clock strikes 10.

Time taken for 9 intervals = 18 seconds.

Time taken for 1 interval = 2s

In order to strike 14, there are 13 intervals, for which the time taken is (13 ×2)=26 s

10. At what time between 4 and 5’o clock will the hands of a clock be together?

(a)

(b)

(c)

(d) none of these

**Answer: (c)**

**Explanation:**

At 4’o clock, the hour hand is at 4 and the minute hand is at 12, i. e. , they are 20 min spaces apart.

To be together, the minute hand must gain 20 minutes over the hour hand.

Now, 55 minutes are gained in