Question

A, B and C are three pipes attached to a cistern. A and B can fill it in 20 minutes and 30 minutes respectively, while C can empty it in 15 minutes. If A, B and C be kept open successively for 1 minute each, how soon will the cistern be filled?

• A. 180 minutes
• B. 60 minutes
• C. 157 minutes
• D. 155 minutes

Answer 1

Answer: (A)

180 minutes

Answer 2

Part filled by A, B and emptied by C in one minute $=\frac{1}{20},\frac{1}{30}$ and $\frac{1}{15}$

Part filled by three pipes in 3 minutes $=\frac{1}{20}+\frac{1}{30}-\frac{1}{15}$

⇒ $\frac{3+2-4}{60}=\frac{1}{6}$

Cistern can be filled in 60 x 3 = 180 minutes.

Hence, option A is the correct answer.The correct option is (A): 180 minutes