Pipes A, B, C fill a tank in 30, 20, and 10 minutes. All are opened for 3 minutes into an empty tank. A, B, C deliver solutions P, Q, R respectively. What fraction of the tank's liquid is solution R after 3 minutes?

Problem restatementEach pipe pours its own solution; find R's proportion after 3 minutes of simultaneous inflow.

Given data

• A rate = 1/30 per min ⇒ 3 min gives 1/10 tank of P
• B rate = 1/20 per min ⇒ 3 min gives 3/20 tank of Q
• C rate = 1/10 per min ⇒ 3 min gives 3/10 tank of R

Concept/ApproachProportion of R = (volume from C) / (total volume after 3 min). No mixing losses.

Step-by-step calculationTotal filled = 1/10 + 3/20 + 3/10 = 2/20 + 3/20 + 6/20 = 11/20R contributed = 3/10 = 6/20Proportion R = (6/20) / (11/20) = 6/11

Common pitfallsDividing C's rate by total rates, instead of using 3-minute volumes.

Final Answer6/11