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?

Explanation:-

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