A pump can fill a tank with water in 2 hours. | vedclass

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(D) Let the capacity of the tank be $1$ unit.The rate of the pump is $\frac{1}{2}$ tank per hour.The effective rate with the leak is $\frac{1}{2 \frac

Vedclass · Accepted Answer

$14$

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(D) Let the capacity of the tank be $1$ unit.The rate of the pump is $\frac{1}{2}$ tank per hour.The effective rate with the leak is $\frac{1}{2 \frac{1}{3}} = \frac{1}{7/3} = \frac{3}{7}$ tank per hour.Let the rate of the leak be $\frac{1}{x}$ tank per hour,where $x$ is the time taken to drain the tank.The effective rate is given by: $	ext{Rate of pump} - 	ext{Rate of leak} = 	ext{Effective rate}$.$\frac{1}{2} - \frac{1}{x} = \frac{3}{7}$.Rearranging the equation: $\frac{1}{x} = \frac{1}{2} - \frac{3}{7}$.$\frac{1}{x} = \frac{7 - 6}{14} = \frac{1}{14}$.Therefore,$x = 14$ hours.

$A$ pump can fill a tank with water in $2$ $hours$. Because of a leak,it took $2 \frac{1}{3}$ $hours$ to fill the tank. The leak can drain all the water of the tank in (in $hours$)?

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