Question

Two pipes A and B can fill a cistern in 37$\frac{1}{2}$ minutes and 45 minutes respectively. Both pipes are opened simultaneously. After what time should the pipe B be turned off such that the cistern will be filled in half an hour?

• A. 5 min
• B. 9 min
• C. 10 min
• D. 15 min
• E. 18 min

Answer 1

The correct option is B

9 min

Let pipe B be turned off after x minutes.

Then, Part filled by (A + B) -in x min. + Part filled by A in (30 - x) min. = 1

$\begin{array}{c}\therefore x\left(\frac{2}{75}+\frac{1}{45}\right)+\left(30-x\right)\frac{2}{75}=1\\ \frac{11x}{225}+\frac{\left(60-2x\right)}{75}=1\\ 11x+180-6x=225\\ x=9\end{array}$