Question

Pipes A and B can fill a cistern in 16 and 24 hours respectively. Pipe C can empty a cistern in 12 hours. How long will it take (in hours) to fill the tank if all the three pipes are opened together?
1. 48
2. 36
3. 72
4. 45

Answer 1

Correct Answer - Option 1 : 48

Given:

Pipe A can fill the cistern = 16 hours

Pipe B can fill the cistern = 24 hours

Pipe C can empty the cistern = 12 hours

Formula used:

Total capacity = LCM

Efficiency = Total Capacity/Time

Concept used:

Efficiency of outlet pipe is always in negative

Calculations:

Total work = LCM (16, 24, 12) = 48 units

Efficiency of pipe A = 48/16 = 3 units

Efficiency of pipe B = 48/24 = 2 units

Efficiency of pipe C = 48/12 = -4 units

When all pipes are opened then effective rate at which tank will fill = 3 + 2 – 4 = 1

Require time = 48/1 = 48 hours

∴ Time taken by A, B and C to fill the tank together is 48 hours