CAT 2018 Slot 1 QA Question 27: A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in

Question

A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in

Accepted Answer

Let the rate of one filling pipe be f and the rate of one draining pipe be d.
$6f - 5d = \dfrac{1}{6}$
$5f - 6d = \dfrac{1}{60}$
Subtract the second equation from the first.
$f + d = \dfrac{1}{6} - \dfrac{1}{60} = \dfrac{3}{20}$
Using $d = \dfrac{3}{20} - f$ in the first equation:
$6f - 5(\dfrac{3}{