Question

Three pipes - A, B, and C are connected to a big tank. Pipes A and B are inlet pipes, while Pipe C is an outlet pipe. A can fill the tank in 12 minutes and B can do the same in 20 minutes, while C can empty the tank in 6 minutes. Pipes A and B are kept open for 5 minutes in the beginning and then pipe C is opened. In what time will the tank be emptied?

• A. 6 minutes
• B. 24 minutes
• C. 9 minutes
• D. 20 minutes

Answer 1

The correct option is D 20 minutes

A can fill $\to \frac{1}{12}$th of the tank in 1 minute

B can fill $\to \frac{1}{20}$th of the tank in 1 minute

Together, A and B can fill $\to \frac{1}{12}+\frac{1}{20}=\frac{4}{30}$th of the tank in 1 minute

In 5 minutes $\to 5\times \frac{4}{30}=\frac{2}{3}$rd of the tank is filled

Water removed when A, B and C are open together $=\frac{1}{6}-\frac{4}{30}=\frac{1}{30}$th in a minute

So, to remove $\frac{2}{3}$rd, it would take $=\frac{2}{3}/\frac{1}{30}=20$minutes