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Clocks and Calendar - Faulty Clock

Clocks and Calendar - Concepts

Clocks and Calendar - Angle Problem

Clocks and Calendar - Calendar Problem

Clocks and Calendar - Faulty Clock

Clocks and Calendar - Clock Problem

Calender Problem Basics

Day of The Week With Reference

Day of The Week Without Reference

Class - HCS Prelims Subjects

Concept Explanation

Clocks and Calendar - Faulty Clock

Faulty Clock Problems : A clock which gains or looses time as compared to correct clock is known as faulty clock. This happens because of the speed of the hands of the clock. A faulty clock gains or loses some minutes in a definite period of time.

For Example : Consider the case of a watch which gains 3 minutes every 2 hours.

If this watch is set at 8 O'clock, then by the time it is actually 10 o'clock, the watch will show 10 hours 3 minutes.

When the faulty clock shows the time to be 12 o'clock , the actual time will be a few minutes to 12.

Let us try to calculate the actual time in the case.

When the actual time elapsed is 2 hours the faulty clock will show 2 hour and 3 minutes on converting into hours we will divide by 60 mins

$=2 ;hours ;3 mins;= 2frac{3}{60}=2frac{1}{20}h=frac{41}{20}h.$

$If; time; elapsed; by ;faulty; clock; is ;frac{41}{20}h; then; actual ;time ;is; 2h$

$If; time; elapsed; by ;faulty; clock; is ;1;h; then; actual ;time ;is; 2timesfrac{20}{41}=frac{40}{41};h$

$If; time; elapsed; by ;faulty; clock; is ;4;h; then; actual ;time ;is; 4timesfrac{40}{41};h$

$If; time; elapsed; by ;faulty; clock; is ;4;h; then; actual ;time ;is; frac{160}{41};h$

So, when the faulty watch shows 12 o'clock (i.e., 4 hours after the watch was set right), the actual time is

$left ( 8+frac{160}{41} right );o;clock= left ( 8+ 3frac{37}{41} right )= left ( 11hr; frac{37}{41} times 60;minright )= 11;hr ;and ;54;min(approx)$

That is approx. 11 hours 54 minutes.

Illustration: A watch, which gains 5 seconds every 3 minutes, is set right at 8 : 00 am. In the afternoon same day, when the faulty watch indicates 5:15, the actual time is

A. 55 minutes past 5 B. 5 o'clock C. 60 minutes past 5 D. 58 minutes past 4

Answer: B

Solution: Actual time (t) : $3times 60 =180$ seconds

False time (T) = $3times 60 +5=185$ seconds

Watch time : 9 hours 15 minutes = $9times60times60+15times60=32400+900=33300$ seconds

$If; false; time; is ;185 ;sec; then; actual ;time ;is; 180 ;sec$

$If; false;time; is ; 1 ;sec; then; actual ;time ;is; frac{180}{185} ;sec$

$If;false; time; is ; 33300;sec; then; actual ;time; is ; frac{180}{185} times 33300;sec$

$If;false; time; is ; 33300;sec; then; actual ;time; is ; 3400;sec= 9 ;hr$

The time was set at 8:00 am so adding 9 to 8:00 am we will get 5:00pm.

Hence the correct option is B

Sample Questions

(More Questions for each concept available in Login)

Question : 1

A watch, which gains 5 seconds every 3 minutes, is set right at 8 : 00 am. In the afternoon same day, when the faulty watch indicates 8:37, the actual time is
A. 8:30 am	B. 8:34 am	C. 8: 36 am	D. 8: 38 am
Right Option : C
View Explanation

Question : 2

A watch, which gains 2 seconds every 5 minutes, is set right at 7 : 00 am. In the afternoon same day, when the faulty watch indicates 9:31, the actual time is _________________
A. 9:30 am	B. 9:35 am	C. 9:38 am	D. 9:40 am
Right Option : A
View Explanation

Question : 3

A watch, which gains 5 seconds every 2 minutes, is set right at 9 : 00 am. On same day, when the faulty watch indicates 9:25, the actual time is
A. 9:20	B. 9:24	C. 9:28	D. 9:30
Right Option : B
View Explanation