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?

$ \dfrac{5}{11} $

$ \dfrac{6}{11} $

$ \dfrac{7}{11} $

$ \dfrac{8}{11} $

Explanation:

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

Part filled by C in 3 minutes =$ \dfrac{3}{10} $.

$\therefore$ Required ratio =$ \left(\dfrac{3}{10} \times\dfrac{20}{11} \right) $=$ \dfrac{6}{11} $.