Question

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?

Accepted Answer

A. Let the total capacity of the tank be $	ext{LCM}(4, 10, 12, 20) = 60$ units. Rate of A $= 60/4 = 15$ units/min. Rate of B $= 60/10 = 6$ units/min. Rate of C $= 60/12 = 5$ units/min. Rate of D $= 60/20 = 3$ units/min. We want the tank to be half-filled (30 units) in 30 minutes, so net filling rate $= 30/30 = 1$ unit/min. Testing option A: Pipe A filling, B, C, D draining: Net rate $= +15 - 6 - 5 - 3 = +1$ unit/min. This satisfies the condition.

Two-way Pipes Tank Filling

Explanation

Practise this under exam conditions