Two pipes A and B can separately fill a ciste | vedclass

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(B) Let the time taken by pipe $C$ alone to empty the full cistern be $x$ $minutes$.The rate of filling by pipe $A$ is $\frac{1}{60}$ of the cistern p

Vedclass · Accepted Answer

$100$

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(B) Let the time taken by pipe $C$ alone to empty the full cistern be $x$ $minutes$.The rate of filling by pipe $A$ is $\frac{1}{60}$ of the cistern per $minute$.The rate of filling by pipe $B$ is $\frac{1}{75}$ of the cistern per $minute$.The rate of emptying by pipe $C$ is $\frac{1}{x}$ of the cistern per $minute$.When all three pipes are opened simultaneously,the net rate of filling is $\frac{1}{50}$ of the cistern per $minute$.Therefore,the equation is: $\frac{1}{60} + \frac{1}{75} - \frac{1}{x} = \frac{1}{50}$.Rearranging the terms to solve for $\frac{1}{x}$:$\frac{1}{x} = \frac{1}{60} + \frac{1}{75} - \frac{1}{50}$.The least common multiple $(LCM)$ of $60, 75,$ and $50$ is $300$.$\frac{1}{x} = \frac{5 + 4 - 6}{300} = \frac{3}{300} = \frac{1}{100}$.Thus,$x = 100$ $minutes$.

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