JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Work, Power & Energy

The ratio of powers of two motors is

\frac{3 x}{x + 1}

, that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of x will be

(A)2
(B)4
(C)2.4
(D)16✓ Correct

Answer: (D)

Solution

Power is the rate of doing work:

P = \frac{m g h}{t}

.

For motor 1:

P_{1} = \frac{300 \times g \times 100}{5 \times 60}

For motor 2:

P_{2} = \frac{50 \times g \times 100}{2 \times 60}

Ratio:

\frac{P _{1}}{P _{2}} = \frac{300}{5 \times 60} \times \frac{2 \times 60}{50} = \frac{300 \times 2}{5 \times 50} = \frac{600}{250} = \frac{12}{5}

Given:

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

Cross-multiply:

12 (x + 1) = 15 x

12 x + 12 = 15 x

12 = 3 x

x = 4

x = 16

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Single correct option

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