# Four two-way pipes A, B, C and D can either fill an empty tank

Four two-way pipes A, B, C and D can either fill an empty tank or drain the full tank in 4, 10, 12 and 20 minutes respectively. All four pipes were opened simultaneously when the tank is empty. Under which of the following conditions the tank would be half filled after 30 minutes?

1. Pipe A filled and pipes B, C and D drained
2. Pipe A drained and pipes B, C and D filled
3. Pipes A and D drained and pipes B and C filled
4. Pipes A and D filled and pipes B and C drained
5. None of the above

Let the capacity of the tank be 60 litres (LCM of 4, 10, 12 and 60).

Pipe A can fill or drain 60/4 or 15 litres in 1 minute.

Similarly, pipes B, C and D can fill or drain 6 litres, 5 litres and 3 litres in 1 minute respectively.

We want to fill the tank half, which is 30 litres, in 30 minutes. This is equal to 1 litre in 1 minute.

Case A: 15 - 6 - 5 - 3 = 1

Case B: 6 + 5 + 3 - 15 = -1

Case C: 6 + 5 - 15 - 3 = -7

Case D: 15 + 3 - 6 - 5 = 7

The correct option is A.