Question

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

• A. $50\%$
• B. $0\%$
• C. $66.66\%$
• D. $33.33\%$

Answer 1

The correct option is D $33.33\%$

Let the initial power be $P_1$ and the final power be $P_2$. Let the initial and final time be $t_1$ and $t_2$ respectively.

$\Rightarrow P_2=P_1+50\%\times P_1$

$=P_1+\frac{P_1}{2}=\frac{3P_1}{2}$

$\Rightarrow P_2=\frac{3P_1}{2}$

We know that,

Power $=\frac{\text{Work done}}{\text{Time}}\Rightarrow P=\frac{W}{t}$

$\therefore W=P\times t$

If work done is constant, $P_1{t}_1=P_2{t}_2$
$\Rightarrow \frac{t_2}{t_1}=\frac{P_1}{P_2}=\frac{2}{3}$
$\Rightarrow t_2=\frac{2}{3}{t}_1$

Decrease in time $=t_1-t_2=t_1-\frac{2}{3}{t}_1=\frac{t_1}{3}$

$\%\text{Decrease in time}$

$=\frac{\text{Decrease in time}}{\text{Initial time}}\times 100$

$=\frac{\left(\frac{t_1}{3}\right)}{t_1}\times 100=\frac{t_1}{3t_1}\times 100=33.33\%$