Question

A tank has 3 pipes. The first pipe can fill $\frac{1}{2}$ part of the tank in 1 hour and the second pipe can fill $\frac{1}{3}$ part in 1 hour. The third pipe is for making the tank empty. When all the three pipes are open, $\frac{7}{12}$ part of the tank is filled in 1 hour. How much time will the third pipe take to empty the completely filled tank?

• A. $3$ hours
• B. $4$ hours
• C. $5$ hours
• D. $6$ hours

Answer 1

The correct option is B $4$ hours

Let the time taken by the third pipe to completely empty the tank $=x$ hours.

Then,
$\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{x}\right)=\frac{7}{12}$

$\Rightarrow \frac{5}{6}-\frac{1}{x}=\frac{7}{12}\Rightarrow \frac{1}{x}=\frac{5}{6}-\frac{7}{12}=\frac{3}{12}=\frac{1}{4}$

So, in 1 hour the tank get emptied by $\frac{1}{4}$th part.

$\therefore$ The third pipe shall take $4$ hours to empty the completely filled tank.