Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minu

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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?

Options:

A . \(\frac{5}{11}\)

B . \(\frac{6}{11}\)

C . \(\frac{7}{11}\)

D . \(\frac{8}{11}\)

Answer: Option B

Part filled by (A + B + C) in 3 minutes = 3 \(\left(\frac{1}{30}+\frac{1}{20}+\frac{1}{10}\right)=\left(3\times\frac{11}{60}\right)=\frac{11}{20}\)

Part filled by C in 3 minutes = \(\frac{3}{10}\)

So, Required ratio = \(\left(\frac{3}{10}\times\frac{20}{11}\right)=\frac{6}{11}\)

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