Question

Two pipes P and Q can fill a tank in 6 hours and 9 hours respectively, while a third pipe R can empty the tank in 12 hours. Initially, P and R are open for 4 hours. Then P is closed and Q is opened. After 6 more hours R is closed. The total time taken to fill the tank (in hours) is _____

• A. 16.50 hrs
• B. 15.50 hrs
• C. 14.50 hrs
• D. 13.50 hrs

Answer 1

The correct option is C 14.50 hrs

$\text{In 1 hour P can fill}=\frac{1}{6}$

$\text{In 1 hour Q can fill}=\frac{1}{9}$

$\text{In 1 hour R can empty}=\frac{1}{12}$

In 4 hour (P+R) can fill
$=4\times (\frac{1}{6}-\frac{1}{12})=\frac{1}{3}$

In 6 hour (Q + R) can fill
$=6(\frac{1}{9}-\frac{1}{12})=\frac{1}{6}$

$\text{In 10 hour tank can fill}=\frac{1}{3}+\frac{1}{6}=\frac{1}{2}$

$\text{Remaining part of tank}=1-\frac{1}{2}=\frac{1}{2}$

$\frac{1}{2}\text{tank Q can fill}=\frac{1}{2}\times 9=4.5hour$

Total time = 10 + 4.5
= 14.5 hours