The ratio of powers of two motors is $\frac{3 \sqrt{x}}{\sqrt{x} + 1}$ , that are capable of raising 300kg water in 5 minutes and 50kg water in 2 minutes respectively from a well of 100m deep. The value of x will be

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2.4

answer is B.

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Detailed Solution

$\frac{P_{1}}{P_{2}} = \frac{\frac{m_{1} {gh}_{1}}{t_{1}}}{\frac{m_{2} {gh}_{2}}{t_{2}}} = \frac{3 \sqrt{x}}{\sqrt{x} + 1} = \frac{300}{5} \times \frac{2}{50}$

$= \frac{3 \sqrt{x}}{\sqrt{x} + 1} = \frac{12}{5}$

$12 \sqrt{x} + 12 = 15 \sqrt{x}$

$12 = 3 \sqrt{x}$

$x = 16$

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