1.

How many times do the hands of a clock coincide in a day?

**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).
==> The hands coincide 22 times in a day.**

2.

How many times are the hands of a clock at right angles in a day?

**Answer: Option 'B'**

**In 12 hours, they are at right angles 22 times.
=> In 24 hours, they are at right angles 44 times.**

3.

How much does a watch lose per day, if its hands coincide every 64 minutes?

**Answer: Option 'A'**

**55 min. spaces are covered in 60 min.
60 min spaces are covered in (60/55 × 60)min = 65 5/11 min
Loss in 64 min = ( 65 5/11- 64 ) = 16/11 min
Loss in 24 hrs = ( 16/11 × 1/64 × 24 × 60 ) min
= 32 8/11 min**

4.

How many times in a day the hands of a clock are straight?

**Answer: Option 'D'**

**In 12 hours, the hands coincide or are in oppesite direction 22 times.
In 24 hours, they are at right angles 22 times.**

5.

At what time between 4 & 5 will the hands of a watch point in opposite directions?

**Answer: Option 'C'**

**At 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30min. spaces apart.
Minute hand will have to gain 5 min. spaces.
55min spaces are gained in 60 min.
5 min. spaces are gained in (60/55 × 50) min. or 54 6/11 min.
Required time = 54 6/11 min. past 4.**

6.

At what time between 9&10 will the hands of a watch be together?

**Answer: Option 'B'**

**To be together between 9 and 10 O'clock, the minute hand has to gain 45min.
spaces 55min. spaces are gained in 60min.
45min.spaces are gained in (60/55 × 45) min. or 49 1/11 min.
The hands are together at 49 1/11 min. past 9.**

7.

At what time between 5.30 & 6 will the hands of a watch be at right angle?

**Answer: Option 'A'**

**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 55min. spaces are gained in 60min.
4min. spaces are gained in (60/55 × 40) min. = 43 7/11min.
Required time = 43 7/11min.past 5.**

8.

At what time between 7 & 8 o'clock will the hands of a watch be in the straight line but no together?

**Answer: Option 'B'**

**When the hands of the clock are in the same straight line but not
togerther, they are 30 minute spaces apart.
At 7 o'clock, they are 25min. spaces apart.
Minute hand will have to gain only 5 min.
space 55 min. spaces are gained in 60min.
5min. spaces are gained in ( 60/55 × 5) min = 5 5/11 min.
Required time = 5 5/11 min. past 7.**

9.

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

**Answer: Option 'D'**

**Angle traced by the hour hand in 6 hours = ( 360/12 × 11/3 )degrees
=180º**

10.

How much watch gain or lose per day, If its hands coincide every 64 min’s?

**Answer: Option 'D'**

**55 min. spaces are covered in 60 min.
60 min. spaces are covered in (60/55 × 60) min = 65 5/11min
Loss in 64min = (65 5/11 - 64) = 16/11 min
Loss in 24 hrs= (16/11 × 1/64 × 24 × 60 ) min = 32 8/11 min. **

11.

Between 4 & 5 O'clock, the time when the hands coincide is:

**Answer: Option 'A'**

**4 × 30 = 120 + 0 × 2/11
=> 240/11 = 21 9/11min **

12.

At what angle the hands of a clock are inclined at 15 minutes past 5?

**Answer: Option 'A'**

**Angle traced by hour hand in 21/4 hrs = ( 360/12 × 21/4)º = 157 1/2º
Angle traced by min. hand in 15min. = ( 360/12 × 15 )º = 90º.
Required angle = ( 157 1/2 )º - 90º = 67 1/2º**

13.

My watch gains 5 min every hour. How many degrees the second hand moves in every min?

**Answer: Option 'B'**

**390º**

14.

A clock is set right at 5am the clock loses 16min in 24 hours. What will be the right time when the clock indicates 10am? On the 4th day?

**Answer: Option 'B'**

**Time from 5am. On a day to 10pm. on 4th day = 89 hours.
Now 23 hrs 44 min. of this clock = 24 hours of correct clock
365/15 hrs of this clock = 24 hours of correct clock
89 hrs of this clock = ( 24 × 15/356 × 89) hrs of correct clock
= 90 hrs of correct clock.
So, the correct time is 11pm. **

15.

When the time in the clock is 7.20, then the angle between the hands of the clock is:

**Answer: Option 'A'**

**7:20
7:4
7~4 = 3 × 20 = 90 + 10 = 100º **

16.

The angle between the minute hand and the hour hand of the clock when the time is 4:20 is ?

**Answer: Option 'B'**

**Angle traced by hour hand in 13/3 hrs = (360/12) x (13/3) = 130º.
Angle traced by minute in 20 minutes =(360/12) x (20) = 120º.
Required angle is = 130º – 120º = 10º**

17.

A clock started at noon. By 10 minutes past 5, the hour hand has turned through?

**Answer: Option 'A'**

**Angle traced by hour hand in 12 hours = 360º.
Angle traced by hour hand in 5 hrs 10 min = 31/6 hrs = (360/12) x (31/6) = 155º**

18.

An accurate clock shows 9 'o' clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 3 'o' clock in the afternoon?

**Answer: Option 'B'**

**Angle traced by the hour hand in 6 hours = (360/12) x 6 = 180º**

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