Question

There are two pipes attached to a tank. Pipe A can fill the tank in 6 hours while B can empty a filled tank in 8 hours. A starts filling the tank and after 4 hours B is also opened. Calculate the total time required to fill the tank.

1. 34/7 hours
2. 12 hours
3. 14 hours
4. 36/7 hours
5. 38/7 hours

Answer 1

Correct Answer - Option 2 : 12 hours

Given:

Pipe A can fill the tank in 6 hours

B can empty a filled tank in 8 hours

Concept used:

Work = time × efficiency

Calculation:

Work	Time	Efficiency
A	6 hours	24/6 = 4
B	8 hours	24/8 = 3
Total work (LCM of time)	24 units

Amount of work done by A in first 4 hours = 4 × 4 = 16 units 

Remaining work = 24 - 16 = 8 units

Now, both A and B are working together, total efficiency = 4 - 3 = 1

Time taken to finish work = work/efficiency = 8/1

Total time taken = 4 + 8 = 12 hours

∴ Total time taken is 12 hours.