P, Q and R are channels which discharge solutions A, B, C respectively in a tank. When the tank is empty and all the three channels are opened what is the proportion of the solution C in the tank after 3 minutes, if the channels P, Q and R can fill the tank from empty to full in 30 minutes and 20 minutes and 10 minutes respectively when they are opened one at a time.
Part filled by (A + B + C) in 3 minutes = 3 $$\times$$ ($$\frac{1}{30} +\frac{1}{20}+Â \frac{1}{10}$$)
= $$\frac{33}{60} = \frac {11}{20}$$
When c works for 1 min its work done in 1 min =Â $$\frac{1}{10}$$
so when it works for 3 min its contribution =Â $$\frac{3}{10}$$
Required ratio = $$\frac{3}{10}\times \frac{20}{11} = \frac{6}{11}$$
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