# 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:

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

 A) 57.5 degrees B) 67.5 degrees C) 77.5 degrees D) 87.5 degrees

Explanation:

Angle traced by hour hand in$214$ 21 hrs = $36012×2140$ =$157102$

Angle traced by min. hand in 15 min = $36012×150$ = $900$

$\inline \fn_jvn \therefore$ Required Angle = $157120-900$ = $67102$

99 37301
Q:

At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?

 A) 11 4/11 B) 13 4/11 C) 15 4/11 D) 16 4/11

Explanation:

At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.
To be coincident, it must gain 15 min. spaces.55 min. are gained in 60 min.
15 min. are gained in
= (60/55 x 15)min
=16+4/11
The hands are coincident at 16 + 4/11 min past 3

54 35401
Q:

The angle between the minute hand and the hour hand of a clock when the time is 8:30

 A) 80 Degrees B) 75 Degrees C) 60 Degrees D) 105 Degrees

Explanation:

Angle traced by hour hand in 17/2 hrs = $36012×172o$ = 255

Angle traced by min hand in 30 min = $36060×30o$ = 180

Therefore,  Required angle = (255 - 180) = $75o$

94 34858
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.

97 32765
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 = $3600-31212-1500=3600-162102=197102$

85 31882
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.

100 29251
Q:

An accurate clock shows 7 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 3 o'clock in the afternoon?

 A) 144º B) 168º C) 180º D) 150º

Explanation:

Angle traced by the hour hand in 6 hours =$360o12×6$ = $180o$.

Filed Under: Clocks - Quantitative Aptitude - Arithmetic Ability
Exam Prep: CAT
Job Role: Bank Clerk

52 28836
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