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

Answer: Option B

Solution(By Examveda Team)

Part filled by (A + B + C) in 3 minutes
$$\eqalign{ & = 3\left( {\frac{1}{{30}} + \frac{1}{{20}} + \frac{1}{{10}}} \right) \cr & = {3 \times \frac{{11}}{{60}}} = \frac{{11}}{{20}} \cr & {\text{Part}}\,{\text{filled}}\,{\text{by}}\,{\text{C}}\,{\text{in}}\,{\text{3}}\,{\text{minutes}} = \frac{3}{{10}} \cr & \therefore {\text{Required}}\,{\text{ratio}} \cr & = {\frac{3}{{10}} \times \frac{{20}}{{11}}} = \frac{6}{{11}} \cr} $$

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