Question

Three pipes named Pipe A, Pipe B and Pipe C are using to fill/drain a tank. It takes 15 hrs to fill the tank if only Pipe A and Pipe B opened. And it will take 20 hrs if Pipe A and Pipe B  are used to fill the tank and Pipe C to drain. How much time will it take if all pipes used to fill the tank?
1. 9
2. 10
3. 12
4. 13

Answer 1

Correct Answer - Option 3 : 12

Calculation:

1/A + 1/B = 1/15      ---(1)

1/A + 1/B - 1/C = 1/20      ---(2)

(1) - (2) gives

⇒ 1/C = 1/15 - 1/20 = 4/60 - 3/60 = 1/60

1/A + 1/B + 1/C = 1/15 + 1/60 = 5/60 = 1/12

12 hrs is needed to fill the tank if all the pipes were opened.

If A, B and C are the time taken by three pipes then the filling/draining rate if three of them opened together is 1/A + 1/B + 1/C.

If any of them used the opposite to others give a negative sign to its rate. For example, if A and B are filling C is draining the tank effective filling rate is 1/A + 1/B - 1/C