# 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:

The reflex angle between the hands of a clock at 10.25 is

 A) 197 1/2 B) 167 1/2 C) 157 1/2 D) 187 1/2

Explanation:

Angle traced by hour hand in 125/12 hrs = (360/12 * 125/12) = $312102$

Angle traced by minute hand in 25 min = (360/60 * 25) = $1500$

$\inline \therefore$ Reflex angle = $3600-31212-1500=3600-162102=197102$

69 30575
Q:

A watch gains 5 seconds in 3 minutes and was set right at 8 AM. What time will it show at 10 PM on the same day ?

 A) 10 : 27 : 41 AM B) 8 : 51 : 04 AM C) 9 : 45 : 15 PM D) 10 : 23 : 20 PM

Explanation:

The watch gains 5 seconds in 3 minutes = 100 seconds in 1 hour.

From 8 AM to 10 PM on the same day, time passed is 14 hours.

In 14 hours, the watch would have gained 1400 seconds or 23 minutes 20 seconds.

So, when the correct time is 10 PM, the watch would show 10 : 23 : 20 PM

52 30378
Q:

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

 A) 32 8/11 B) 33 8/11 C) 34 8/11 D) 35 8/11

Explanation:

55min spaces are covered in 60min

60 min. spaces are covered in (60/55 x 60) min= 65+5/11 min.

loss in 64min=(65+5/11)- 64 =16/11

Loss in 24 hrs (16/11 x 1/64 x 24 x 60) min= 32 8/11.

88 29587
Q:

At what time between 3 and 4 o’clock will the minute hand and the hour hand are on the same straight line but facing opposite directions ?

 A) 3:15 2/8 B) 3:49 C) 3:49 1/11 D) 3:51

Explanation:

On straight line means 180 degree angle.
180 = 11/2 min – 30 hrs
180 = 11/2 m – 30 × 3
180 = 11/2 m – 90
(180 + 90) 2 = 11 m
m = 540/11 = 49 1/11 minutes.

30 27458
Q:

In 16 minutes, the minute hand gains over the hour hand by -

 A) 16 deg B) 80 deg C) 88 deg D) 94 deg

Explanation:

In one hour, the minute hand gains 330° over the hour hand. i.e., 60 minute, the minute hand gains 330° over the hour hand.

∴ In 16 minutes, the minute hand gain over the hour hand by

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Q:

A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is:

 A) 4pm B) 5pm C) 6pm D) 7pm

Explanation:

Time from 7 am to 4.15 pm  = 9 hrs 15 min = $374$ hrs

3 min. 5 sec. of this clock = 3 min. of the correct clock.

Now 3min.5sec. is$37720$ hrs of this clock = 3 min.is$120$ hrs of the correct clock

$374$ hrs of clock = $120×72037×374$ hrs of the correct clock.

= 9 hrs of the correct clock.

$\inline \therefore$ The correct time is 9 hrs after 7 am. i.e., 4 pm.

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Q:

At what time, between 3 o’clock and 4 o’clock, both the hour hand and minute hand coincide each other  ?

 A) 3:16 7/11 B) 3:16 11/4 C) 3:30 D) 3:16 4/11

Explanation:

Coincide means 00  angle.

This can be calculated using the formulafor time A to B means  [11m/2 - 30 (A)]

Here m gives minutes after A the both hands coincides.

Here A = 3, B = 4

0 =11m/2 –30 × 3
11m = 90 × 2 = 180
m= 180/11 = 16 4/11

So time = 3 : 16 4/11

35 22903
Q:

How many degrees will the minute hand move, in the same time in which the second hand move 4800 ?

 A) 80 deg B) 160 deg C) 140 deg D) 135 deg