Three pipes A, B and C  can fill a tank in 72 minutes. If all the three pipes remain opened for 36 minutes and then pipe C is closed it took 1 hour more to fill the tank by pipes A and B. What is the time required to fill the tank by pipe C alone?

3 hrs

The correct answer is option (2) : 3hrs

Part of tank filled by A, B and C in 1 min $=\frac{1}{72}$

Part of tank filled by A, B and C in 36 min $=\frac{36}{72}=\frac{1}{2}$

Remaining part $=1-\frac{1}{2}=\frac{1}{2}$

In 1 hr i.e 60 min and B can fill $=\frac{1}{2×60}=\frac{1}{120}$ part of tank.

Now, C's 1 min work = (A+B+C)'s  1min work - (A+B)'s 1 min work

$⇒\frac{1}{72}-\frac{1}{120}=\frac{4}{120}=\frac{1}{180}$

Hence, C alone can fill the tank in 180 min i.e 3 hrs