Question

A chemical plant has four tanks (A, B, C and D), each containing 1000 litres of a chemical. The chemical is being pumped from one tank to another as follows:

From A to B @ 20 litres/minute
From C to A @ 90 litres/minute
From A to D @ 10 litres/minute
From C to D @ 50 litres/minute
From B to C @ 100 litres/minute
From D to B @ 110 litres/minute

Which tank gets emptied first, and how long does it take (in minutes) to get empty after pumping starts?

Accepted Answer

C. Let us calculate the net inflow/outflow rate for each tank: - Net rate for A = Inflow from C (90) - Outflow to B (20) - Outflow to D (10) = $+60$ litres/min - Net rate for B = Inflow from A (20) + Inflow from D (110) - Outflow to C (100) = $+30$ litres/min - Net rate for C = Inflow from B (100) - Outflow to A (90) - Outflow to D (50) = $-40$ litres/min - Net rate for D = Inflow from A (10) + Inflow from C (50) - Outflow to B (110) = $-50$ litres/min Since tank D has the maximum rate of depletion (50 litres/minute), it will get emptied first. Time taken for D to empty = $\frac{1000}{50} = 20$ minutes.

Chemical plant tank emptying

Explanation

Practise this under exam conditions