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A pump can fill a tank with water in 3 hours. Because of a leak it took \(3\frac{1}{5}hours\) to fill the tank. The leak can drain all the water in the tank in
A pump can fill a tank with water in 3 hours. Because of a leak it took \(3\frac{1}{5}hours\) to fill the tank. The leak can drain all the water in the tank in
1). 54 hours
2). 36 hours
3). 42 hours
4). 48 hours
1 answers
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The pump can fill the tank in 3 hours
∴ Part of tank filled by the pump in 1 hour = 1/3
Let, the leak can drain all the water in ‘x’ hours
∴ Part of tank leaked by the drain in 1 hour = 1/x
Given, Because of a leak pump took $(3\frac{1}{5}hours = \frac{{16}}{5}hours)$ to fill the tank
$(\therefore \frac{1}{3} \times \frac{{16}}{5} - \frac{1}{x} \times \frac{{16}}{5} = 1)$
⇒ 16/15 - 16/5x = 1
⇒ 16/5x = 16/15 – 1 = 1/15
⇒ 5x = 16 × 15
⇒ x = 48 hours