Two pipes A and B can fill a cistern in 15 minutes and 30 minutes respectively. Both pipes are opened together, but after 5 minute pipe B is turned off. The cistern will be full in total:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) - 12.5 minutes
$\text{Rate of A} = \frac{1}{15},\;\; \text{Rate of B} = \frac{1}{30}$
$\text{Together rate} = \frac{1}{15} + \frac{1}{30} = \frac{1}{10}$
$\text{Work done in 5 minutes} = 5 \times \frac{1}{10} = \frac{1}{2}$
$\text{Remaining work} = 1 - \frac{1}{2} = \frac{1}{2}$
$\text{Now only A works}$
$\text{Time} = \frac{\frac{1}{2}}{\frac{1}{15}} = \frac{1}{2} \times 15 = 7.5 \text{ minutes}$
$\text{Total time} = 5 + 7.5 = 12.5 \text{ minutes}$
The cistern will be full in $12.5$ minutes.