Test: Clocks- 2 - CAT MCQ

We know that angle traced by hour hand in 12 hrs = 360°

From 8 to 2, there are 6 hours.

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

We know that angle traced by hour hand in 12 hrs = 360° 

Time duration from noon to 10 minutes past 5
= 5 hours 10 minutes

Hence the angle traced by hour hand from noon to 10 minutes past 5

Angle between hands of a clock 

When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock

When the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H 'o clock

The hands of a clock coincide 11 times in every 12 hours (Between 11 and 1, they coincide only once, at 12 o'clock).

12:00 am
1:05 am
2:11 am
3:16 am
4:22 am
5:27 am
6:33 am
7:38 am
8:44 am
9:49 am
10:55 am
12:00 pm
1:05 pm
2:11 pm
3:16 pm
4:22 pm
5:27 pm
6:33 pm
7:38 pm
8:44 pm
9:49 pm
10:55 pm

Hence the hands coincide 22 times in a day.

This is already given as a formula and it's is better to learn the answer by heart as 22 which can save time in competitive exams.(However you should know the theory behind).

The two hands of a clock will be in the same straight line but not together between HHand (H+1)(H+1) o' clock at

Here H = 4. Hands of the watch will point in opposite directions at 

Time from 5 am to 10 pm on the 4th day 
= 3 days 17 hours 
= 3 × 24 + 17 
= 89 hours.

Given that clock loses 16 minutes in 24 hours.

If the minute hand of a clock overtakes the hour hand at intervals of MM minutes of correct time, the clock gains or loses in a day by

Here M = 65. The clock gains or losses in a day by

At 4 o' clock, the hands are 20 minute spaces apart.

To get the first 4 min spaces between the hands ,the minute hand has to gain 20 - 4 = 16 minute spaces over the hour hand.

To get the second 4 min spaces between the hands ,the minute hand has to gain 20 + 4 = 24 minute spaces over the hour hand.

In 60 minutes, minute hand gains 55 minute spaces over the hour hand.

Time taken for gaining 16 minute spaces by minute hand

Angle between hands of a clock 

When the minute hand is behind the hour hand, the angle between the two hands at MM minutes past HH 'o clock

When the minute hand is ahead of the hour hand, the angle between the two hands at MM minutes past HH 'o clock

Here H = 4, M = 40 the minute hand is ahead of the hour hand. Hence the angle