# Clocks Questions

FACTS  AND  FORMULAE  FOR  CLOCKS  QUESTIONS

The face or dial of a watch is a circle whose circumference is divided into 6 equal parts, called minute spaces.

A clock has two hands, the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand.

1. In 60 minutes, the minute hand gains 55 minutes on the hour on the hour hand.

2. In every hour, both the hands coincide once.

3. The hands are in the same straight line when they are coincident or opposite to each other.

4. When the two hands are at right angles, they are 15 minute spaces apart.

5. When the hands are in opposite directions, they are 30 minute spaces apart.

6. Angle traced by hour hand in 12 hrs = 360°

7. Angle traced by minute hand in 60 min. = 360°.

Too Fast And Too Slow : If a watch or clock indicated 8.15, when the correct time is 8, it is said to be 15 minutes too fast.

On the other hand, if it indicates 7.45, when the correct time is 8, it is said to be 15 minutes too slow.

Q:

In every 60 minutes, the minute hand gains -------- minutes on the
hour hand

 A) 53 B) 54 C) 55 D) 56

Explanation:

point to be remembered

26 17410
Q:

At 3.40, the hour hand and the minute hand of a clock form an angle of:

 A) 110 B) 120 C) 130 D) 140

Explanation:

Angle traced by hour hand in 12 hrs. = 360º.

Angle traced by it in $113$hrs =$36012×1130$$1100$

Angle traced by minute hand in 60 min. = $3600$

Angle traced by it in 40 min = $36060×400$$2400$

$\inline \fn_jvn \therefore$Required angle (240 - 110)º = $1300$

20 12397
Q:

The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:

 A) 0 B) 10 C) 30 D) 60

Explanation:

Angle traced by hour hand in $133$hrs = $36012×1330$$1300$

Angle traced by min. hand in 20 min = $36060×200$ =$1200$

Required angle = (130 - 120)º = 10º

23 12206
Q:

When the hands are in the opposite directions,they are ------- minute spaces apart,

 A) 15 B) 30 C) 60 D) 0

Explanation:

24 11308
Q:

What is the ratio of 18 minutes to one hour ?

 A) 1/5 B) 3/4 C) 1/7 D) 3/10

Explanation:

One hour = 60 min

18/60 = 3/10

44 10334
Q:

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

 A) 36 7/9 min B) 32 8/11 min C) 34 3/11 min D) 65 5/11 min

Explanation:

55 min. spaces are covered in 60 min.

60 min. spaces are covered in min. = min.

Loss in 64 min. = min.

Loss in 24 hrs = min. = min.

38 10334
Q:

The angle between the minute hand and the hour hand of a clock when the time is 4.15 is

 A) 0 B) 37.5 C) 27 D) 15

Explanation:

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

=> $30H-M5+M2$ degrees

Here H = 4, M = 15 and the minute hand is behind the hour hand.

Hence the angle

= 30[4-(15/5)]+15/2 = 30(1)+7.5 = 37.5 degrees

28 9688
Q:

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 ?

 A) 2 p.m on Tuesday B) 2 p.m on Wednesday C) 3 p.m on Thursday D) 1 p.m on Friday

Explanation:

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

Therefore, The watch gains $2+445$ min. or  34/5 min. in 170 hrs.

Now, 34/5 min. are gained in 170 hrs.

Therefore, 2 min are gained in $170×534×2$ hrs = 50 hrs

Therefore, 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.