A cistern has two taps which fill it in $12$ minutes and $15$ minutes respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in $20$ minutes. How long will the waste pipe take to empty the full cistern ?

A) 20 minutes

B) 30 minutes

C) 40 minutes

D) 50 minutes

E) 10 minutes


Option E


Work done by the waste pipe in $1$ minute $=\left[\frac{1}{20}-\left(\frac{1}{12}+\frac{1}{15}\right)\right]$ $=-\frac{1}{10}$

Waste pipe will empty the full cistern in 10 minutes.