Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

Question: Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?

Solution:
Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10)
= 3(2 + 3 + 6)/60
= 3(11/60)
= 11/20

Part filled by C in 3 minutes = 3/10

∴ Required ratio = (3/10) × (20/11)
= 6/11