The ratio of powers of two motors is 3 x x + 1 , that are capable...

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

Power is $P = \dfrac{W}{t}$

Let the powers of both the motors be ${P}_{1} \text{ and } {P}_{2}$ respectively.

Hence, the ratio of the powers is,

$\dfrac{{P}_{1}}{{P}_{2}} = \dfrac{\dfrac{300 \times g \times 100}{5 \times 60}}{\dfrac{50 \times g \times 100}{2 \times 60}} = \dfrac{60}{25} ⇒ \dfrac{3\sqrt{x}}{\sqrt{x} + 1} = 2 . 4$

$⇒ 3\sqrt{x} = 2 . 4\sqrt{x} + 2 . 4$

$⇒ x = 16$