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Question

If power is increased by 50% and work done is constant, then the time taken is reduced by:

A
50%
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B
0%
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C
66.66%
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D
33.33%
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Solution

The correct option is D 33.33%
Let the initial power be P1 and the final power be P2. Let the initial and final time be t1 and t2 respectively.

P2=P1+50%×P1

=P1+P12=3P12

P2=3P12

We know that,

Power =Work doneTimeP=Wt

W=P×t

If work done is constant, P1t1=P2t2
t2t1=P1P2=23
t2=23t1

Decrease in time =t1t2=t123t1=t13

%Decrease in time

=Decrease in timeInitial time×100

=(t13)t1×100=t13t1×100=33.33%

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