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. **

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