Two pipes A and B can fill an empty tank in 10 hours and 15 hours respectively. Pipe C alone can empty the completely filled tank in 12 hours. First both pipes A and B are opened and after 5 hours pipe C is also opened. What is the total time (in hours) in which then tank will be filled?

Solution (By Examveda Team)

According to question,
Efficiency of (A + B) = 18 + 12 = 30 litre/hr
In 5 hrs, filled capacity by (A + B) = 30 × 5 = 150 litres
∴ Remaining capacity = 180 - 150 = 30 litres
Total efficiency of (A + B + C) = 18 + 12 - 15 = 15 litre/hr
∴ Time taken by (A + B + C) to fill the remaining capacity
$$ \Rightarrow \frac{{30}}{{15}} = 2\,{\text{hrs}}$$
∴ Required time, to fill the complete tank = 5 hrs + 2 hrs = 7 hrs