Three pipes A, B and C can fill a tank in 30 | vedclass

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(C) The rate of filling for pipes $A, B,$ and $C$ are $\frac{1}{30}, \frac{1}{20},$ and $\frac{1}{10}$ of the tank per minute,respectively.The total p

Vedclass · Accepted Answer

$\frac{6}{11}$

Vedclass · Answer

(C) The rate of filling for pipes $A, B,$ and $C$ are $\frac{1}{30}, \frac{1}{20},$ and $\frac{1}{10}$ of the tank per minute,respectively.The total part of the tank filled in $1 \ min$ by all three pipes is $\frac{1}{30} + \frac{1}{20} + \frac{1}{10} = \frac{2 + 3 + 6}{60} = \frac{11}{60}$.In $3 \ min$,the total part of the tank filled is $3 	imes \frac{11}{60} = \frac{33}{60} = \frac{11}{20}$.The amount of solution $R$ contributed by pipe $C$ in $3 \ min$ is $3 	imes \frac{1}{10} = \frac{3}{10}$.The fraction of solution $R$ in the total liquid in the tank after $3 \ min$ is $\frac{	ext{Amount of } R}{	ext{Total liquid}} = \frac{3/10}{11/20} = \frac{3}{10} 	imes \frac{20}{11} = \frac{6}{11}$.

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