Clocks and Calendar - Faulty Clock


 
 
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 9 : 00 am. In the afternoon same day, when the faulty watch indicates 5:15, the actual time is ___________________

Right Option : B
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Explanation
Question : 2

A watch which gains uniformly is 4 minutes slow at noon on Monday, and is 4 minute 48 sec fast at 4 pm on the following Wednesday. At what time it was correct?

Right Option : A
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Explanation
Question : 3

A watch, which gains 5 seconds every 3 minutes, is set right at 7 : 00 am. In the afternoon same day, when the faulty watch indicates 4:15, the actual time is

Right Option : B
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Explanation
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