Question

Two taps can separately fill a cistern in 10 minutes and 15 minutes respectively. If these two pipes and a waste pipe are kept open simultaneously, the cistern gets filled in 18 minutes. The waste pipe can empty the full cistern in

• A. 7 minutes
• B. 13 minutes
• C. 23 minutes
• D. 9 minutes

Answer 1

The Correct Option is D

Let, the time taken by waste pipe to empty the cistern \(=\) '\(x\)'

Part filled by two pipes in 1 minute is 1/10 and 1/15 respectively and the cistern gets filled in 18 minutes (given).

Net part filled in 1 hour is given by,

\(\frac{1}{10}+\frac{1}{15}-\frac{1}{x}=\frac{1}{18}\)

\(\frac{1}{10}+\frac{1}{15}-\frac{1}{18}=\frac{1}{x}\)

\(\frac{9+6-5}{90}=\frac{1}{x}\)

\(\frac{10}{90}=\frac{1}{x}\) or \(x=9\) minutes

Hence, option D is the correct answer.The correct option is (D): 9 minutes