Two pipes A and B can fill a tank in 20 and 30 hours respectively. Both the pipes are opened to fill the tank but when the tank is one - third full, a leak develops in the tank through which one - third water supplied by both the pipes gose out. The total time taken to fill the tank is?

Answer: Option C

Part filled by (A + B) in 1 hour
$$\begin{array}{rl}& \text{= }\left(\frac{1}{20}+\frac{1}{30}\right)\\ & =\frac{1}{12}\end{array}$$
So, A and B together can fill the tank in 12 hrs,
$$\frac{1}{3}$$ part is filled by (A + B) in
$$\left(\frac{1}{3}\times 12\right)\text{ = 4 hrs}$$
Since the leak empties one - third water, so time taken to fill the tank
= Time taken by (A + B) to fill the whole tank + Time taken by (A + B) to fill one - third tank
= (12 + 4)
= 16 hours