CAT 2021 Slot 2 QA Question 9: Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Inst

Question

Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Inst

Accepted Answer

Let the filling rate of pipe A be $a$ tank/hour and the draining rate of pipe B be $b$ tank/hour.

In the first case, A works for 8 hours and B works for 7 hours.
$8a-7b=1$

In the second case, A works for 4 hours and B works for 2 hours.
$4a-2b=1$

Multiply the second equation by 2 and subtract the