The ratio of powers of two motors is 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

Step-by-step solution

The work done in raising the water is W = m g h . Power is P = W t Let the powers of both the motors be P 1   &   P 2 respectively. Hence, the ratio of the powers is, P 1 P 2 = 300 × g × 100 5 × 60 50 × g × 100 2 × 60 = 60 25 ⇒ 3 x x + 1 = 2 . 4 ⇒ 3 x = 2 . 4 x + 2 . 4 ⇒ x = 16