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1. 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?

A. $\frac{5}{11}$

B. $\frac{6}{11}$

C. $\frac{7}{11}$

D. $\frac{8}{11}$

Solution:

Part filled by (A + B + C) in 3 minutes

\begin{aligned} = 3 (\frac{1}{30} + \frac{1}{20} + \frac{1}{10}) \\ = 3 \times \frac{11}{60} = \frac{11}{20} \\ Part filled by C in 3 minutes = \frac{3}{10} \\ ∴ Required ratio \\ = \frac{3}{10} \times \frac{20}{11} = \frac{6}{11} \end{aligned}

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