In a certain task, a person has to fill an empty tank using four taps, each of which can fill the entire empty tank in

VJesus12 wrote: ↑

Fri Feb 11, 2022 3:26 am

In a certain task, a person has to fill an empty tank using four taps, each of which can fill the entire empty tank in 1 hour, and once the tank is filled completely, he needs to empty the tank using two outlets, at the bottom of the tank. Both the outlets can empty the full tank at the same time. How much time does an outlet take to empty a full tank, if the total time taken by the person to finish the task is 30 minutes?

A. 1/4 hour
B. 1/3 hour
C. 1/2 hour
D. 3/4 hour
E. 1 hour

Answer: C

Source: e-GMAT

\(1\) tap can fill a tank in \(1\) hour. Then 4 taps can fill the tank in \(\dfrac{1}{4}\) hour

i.e, \(4\) taps fill the tank in 15 minutes. Now, the entire task of filling the tank and emptying the tank is completed in \(30\) minutes. So in \(30\) minutes, the first \(15\) minutes were to fill the tank and the rest \(15\) minutes were to empty the tank.

So \(2\) taps took \(15\) minutes to empty the tank, then each tap takes \(30\) minutes to empty the tank.

\(30\) minutes \(= \dfrac{1}{2}\) hour

Therefore, C