Question

A cistern has two inlets $A$ and $B$ which can fill it in $12$ minutes and $15$ minutes respectively. An outer $C$ can empty the full cistern in $10$ minutes. If all the three pipes are opened together in the empty cistern, time taken to fill the cistern completely is _________.

• A. $20minutes$
• B. $10minutes$
• C. $15minutes$
• D. $5minutes$

Answer 1

Answer: (A)

$20minutes$

Lets calculate contribution of each inlet to fill the cistern,

we will use negative contribution for inlet emptying the cistern.

Let total volume of cylinder be 1 unit.

A's one minute contribution$=\frac{1}{12}$

B's one minute contribution$=\frac{1}{15}$

C's one minute contribution$=-\frac{1}{10}$

(A+B+C)'s one minute contribution in filling the tank$=\frac{1}{12}+\frac{1}{15}-\frac{1}{10}=\frac{(5+4-6)}{60}=\frac{1}{20}$

Time taken by A+B+C to fill 1 unit of volume= $\frac{1}{1/20}min=20min$