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?
A. 12 hours
B. 14 hours
C. 16 hours
D. 18 hours
Answer: Option C
Solution(By Examveda Team)
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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