Question

Two pipes A and B can fill a water tank in 20 minutes and 24 minutes, respectively, and the third pipe C can empty at the rate of 3 gallons per minute. If A, B and C opened together, fill the tank in 15 minutes the capacity (in gallons) of the tank is

• A. 180
• B. 150
• C. 120
• D. 60

Answer 1

The correct option is C 120

Part of the tank filled when all the three pipes are opened in 1 minute $=\frac{1}{15}$

Part of the tank filled when (A + B) are opened in 1 minute $=\frac{1}{20}+\frac{1}{24}=\frac{6+5}{120}=\frac{11}{120}$

$\therefore$ Part of the tank emptied by C in 1 min $=\frac{11}{120}-\frac{1}{15}=\frac{1}{40}$

$\therefore$ Capacity of $=\frac{1}{40}$ part of the tank $=3$ gallons

$\therefore$ Capacity of the tank $=(3\times 40)$ gallons $=120$ gallons