Three pipes A, B and C can fill a tank in 6 hours, 9 hours and 12 hours respectively. B and C are opened for half an hour, then A is also opened. The time taken by the three pipes together to fill the remaining part of the tank is -

Answer: Option C

Solution

Answer: Option C

Solution:

In half an hour (B + C) must have filled
$$=\frac{4}{2}+\frac{3}{2}=\frac{7}{2}\text{units}$$
Capacity left
$$\text{ = 36}-\frac{7}{2}=\frac{65}{2}\text{units}$$
Now all pipes will fill the remaining tank
$$\begin{array}{rl}& \text{ = }\frac{65}{2\times \left(6+4+3\right)}\\ & =\frac{65}{2\times 13}\\ & =\frac{5}{2}\\ & =2\frac{1}{2}\text{hours}\end{array}$$