A tap takes 36 hours extra to fill a tank due to a leakage equivalent to half of its inflow. The inflow can fill in how many hours?
35
37
36
40
Explanation:
Let inflow alone can fill the tank in x hours.
Then, the leak alone can empty the tank in 2x hours.
Part filled by the inflow in 1 hour =$\dfrac{1}{x}$
Part emptied by the leak in 1 hour =$\dfrac{1}{2x}$
Net part filled by the inflow and the leak in 1 hour =$\dfrac{1}{x+36}$
$\dfrac{1}{x}−\dfrac{1}{2x}=\dfrac{1}{x+36}$
⇒$\dfrac{1}{2x}=\dfrac{1}{x+36}$
⇒2x=x+36
⇒x=36