Aptitude Question ID: 105345
A cistern has two pipes. One can fill it with water in 8 hours and other can empty it in 5 hours. In how many hours will the cistern be emptied if both the pipes are open together when $latex \frac{3}{4}&s=1$ of the cistern is already full of water?
[A]$latex 3\tfrac{1}{3}\ hours&s=1$
[B]$latex 6\ hours&s=1$
[C]$latex 10\ hours&s=1$
[D]$latex 13\tfrac{1}{3}\ hours&s=1$
$latex 10\ hours&s=1$
Part of cistern emptied in 1 hour
$latex = \frac{1}{5}-\frac{1}{8}=\frac{8-5}{40} = \frac{3}{40}&s=1$
$latex \because \frac{3}{40}&s=1$ part is emptied in 1 hour.
$latex \therefore \frac{3}{4}&s=1$ part is emptied in $latex \frac{40}{3}\times \frac{3}{4} = 10\ hours&s=1$
Hence option [C] is correct answer.