The ratio of powers of two motors is 3 x x + 1 , that are capable of raising 300   kg water in 5…

The work done in raising the water is $W=mgh$.

Power is $P=\frac{W}{t}$

Let the powers of both the motors be $P_1 \& P_2$ respectively.

Hence, the ratio of the powers is,

$$\begin{gathered} \frac{P_1}{P_2}=\frac{\frac{300\times g\times 100}{5\times 60}}{\frac{50\times g\times 100}{2\times 60}}=\frac{60}{25} \\ \Rightarrow \frac{3\sqrt{x}}{\sqrt{x}+1}=2.4 \end{gathered}$$$$

$\Rightarrow 3\sqrt{x}=2.4\sqrt{x}+2.4$

$\Rightarrow x=16$