CAT 2023 Slot 2 QA Question 11: Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turne

Question

Pipes A and C are fill pipes while Pipe B is a drain pipe of a tank. Pipe B empties the full tank in one hour less than the time taken by Pipe A to fill the empty tank. When pipes A, B and C are turne

Accepted Answer

Let Pipe A fill the tank in $a$ hours and Pipe C fill the tank in $c$ hours. Then Pipe B empties the tank in $a - 1$ hours.

Using rates, the first condition gives:
$\dfrac{1}{a} - \dfrac{1}{a - 1} + \dfrac{1}{c} = \dfrac{1}{2}$

In the second situation, B and C work together for 1 hour, and then C