Two pipe A and B can fill a water tank in 20 and 24 minutes respectively and a third pipe C can empty at the rate of 3 gallons per minute. If A, B and C are open together to fill the tank in 15 minutes, find the capacity of tank?

A. 180 gallons

B. 150 gallons

C. 120 gallons

D. 60 gallons

Answer: Option C

Solution(By Examveda Team)

Work done by the C pipe in 1 minute
$$\eqalign{ & = \frac{1}{{15}} - \left( {\frac{1}{{20}} + \frac{1}{{24}}} \right) \cr & = \left( {\frac{1}{{15}} - \frac{{11}}{{120}}} \right) \cr & = - \frac{1}{{40}}\,\left[ { - {\text{ve}}\,{\text{means}}\,{\text{emptying}}} \right] \cr} $$
∴ Volume of $$\frac{1}{{40}}$$ part = 3 gallons.
Volume of whole = (3 × 40) gallons = 120 gallons.