A pump can fill a tank with water in 2 hours. Because of a leak, it took 2$\dfrac{2}{3}$ hours to fill the tank. The leak can drain all the water of the tank in?
6 hours
8 hours
9 hours
10 hours
Explanation:
Let the leak can drain all the water of the tank in y hours
Part of the tank filled by the pipe in 1 hr = 1/2
Part of the tank emptied by the leak in 1 hr = 1/y
Part of the tank filled by the pipe with leak in 1 hr=$\dfrac{1}{2\dfrac{2}{3}}=\dfrac{1}{\dfrac{8}{3}}=\dfrac{3}{8}$
$\dfrac{1}{2}+(−\dfrac{1}{y})=\dfrac{3}{8}$
$\dfrac{1}{2}−\dfrac{1}{y}=\dfrac{3}{8}$
⇒$\dfrac{1}{y}=\dfrac{1}{2}−\dfrac{3}{8}=\dfrac{1}{8}$
⇒y=8
i.e., the leak can drain all the water of the tank in 8 hours