Discussion
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?
Answer: B
Work out how much each pipe contributes in 3 minutes.
\[ P = \frac{3}{30} = \frac{1}{10}, \qquad Q = \frac{3}{20}, \qquad R = \frac{3}{10} \]
Over the common denominator 20:
\[ \frac{2}{20} + \frac{3}{20} + \frac{6}{20} = \frac{11}{20} \text{ total} \]
\[ \text{proportion of R} = \frac{6/20}{11/20} = \frac{6}{11} \]
The tank is only \( \tfrac{11}{20} \) full at that point, so the proportions are taken against that total rather than against a full tank.
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