Question

Three pipes P, Q and R can fill a tank in 12 minutes, 18 minutes and 24 minutes respectively. The pipe R is closed 12 minutes before the tank is filled. In what time the tank is full?

• A. $\left(8\frac{5}{13}\right)hrs$
• B. $\left(8\frac{4}{13}\right)hrs$
• C. $\left(7\frac{4}{13}\right)hrs$
• D. $\left(8\frac{6}{13}\right)hrs$
• E. None of these

Answer 1

The correct option is B $\left(8\frac{4}{13}\right)hrs$

Let T be the time taken by the pipes to fill the tank
$(\frac{1}{12}+\frac{1}{18}+\frac{1}{24})\times (T-12)+(\frac{1}{12}+\frac{1}{18})\times 12=1$
We will get $T=\frac{108}{13}=8\frac{4}{13}hrs$