Question

If the horse power of an engine $B$ is four times that of the horse power of an engine $A$, then the ratio of the the work done by $A$ and $B$ in the time span of $10min$and $20min$ respectively is _________

• A. $1:2$
• B. $1:4$
• C. $8:1$
• D. $1:8$

Answer 1

The correct option is D

$1:8$

Explanation for correct answer: Option ()

Assumptions:

Power of engine,$A=P_A$

Power of engine,$B=P_B$

Work of engine $A=W_A$

Work of engine $B=W_B$

Time span of engine $A=T_A$

Time span of engine $B=T_B$

Step 1: Given Data

Horse power of an engine $B$ is four times that of the horse power of an engine $A$,

Mathamatically; $P_B=4P_A$

Time span of engine $A=T_A=10min$

Time span of engine $B=T_B=20min$

Step 2: Ratio of work Done

As we know rate of doing work is eqyal to power.or,$Power=\frac{Work}{time}$

So,$PowerofA=\frac{WorkdonebyA\left(W_A\right)}{time\left(T_A\right)}$ and $PowerofB=\frac{WorkdonebyB\left(W_B\right)}{time\left(T_B\right)}$

$$\begin{gathered} \frac{P_A}{P_B}=\frac{W_A}{T_A}\times \frac{T_B}{W_B} \\ \frac{P_A}{4P_A}=\frac{W_A}{10min}\times \frac{20min}{W_B}\Rightarrow \frac{W_A}{W_B}=\frac{1}{4}\times \frac{10}{20} \\ \Rightarrow \frac{W_A}{W_B}=\frac{1}{8} \end{gathered}$$

Hence,the ratio of the the work done by $A$ and $B$$=1:8$