Question

Pipe A can fill a tank in 6 h and B can fill it in 9 h. It takes 24 min more to fill, when a third pipe C is also opened. In how much time C can empty the whole tank alone
1. 36 h
2. 42 h
3. 40 h
4. None

Answer 1

Correct Answer - Option 1 : 36 h

Given:

Time taken by A to fill the tank = 6 h

Time taken by B to fill the same tank = 9 h

Time taken by (A + B + C) to fill the tank = Time taken by (A + B) + 24 min

Concept used:

If a tap can fill a tank in X h, part of the tank filled in 1 h = 1 / X

For outlet pipe, efficiency should be taken with negative sign

Part of the tank filled by A in 1 h = 1 / 6

Part filled by B in 1 h = 1 / 9

Part filled by (A + B) in 1 h = 1 / 6 + 1 / 9 = 10 / 36 = 5 / 18

∴ Time taken by (A + B) to fill the tank = 18 / 5 = 3 h 36 min

∴ Time taken by (A + B + C) to fill the tank = 3 h 36 min + 24 min = 4 h

∴ Part of tank filled by (A + B + C) in 1 h = 1 / 4

Let, C can empty the whole tank in X h

Part of tank empty by C in 1 h = 1 / X

∴ 1 / 6 + 1 / 9 + (-1 / X) = 1 / 4

⇒ 1 / X = 1 / 6 + 1 / 9 – 1 / 4 = 1 / 36

∴ X = 36

Therefore, C can empty the whole tank in 36 h