a) 12 hours
b) 14 hours
c) 16 hours
d) 18 hours
Answer: c
Explanation: Part filled by (A + B) in 1 hour
$$\eqalign{
& {\text{= }}\left( {\frac{1}{{20}} + \frac{1}{{30}}} \right) \cr
& = \frac{1}{{12}} \cr} $$
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
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