A, B and C are three pipes connected to a tan | vedclass

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(D) Let the work done by pipes $A, B$ and $C$ in $1 	ext{ h}$ be $\frac{1}{a}, \frac{1}{b}$ and $\frac{1}{c}$ respectively.Given:$\frac{1}{a} + \frac

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$5 \frac{5}{7} 	ext{ h}$

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(D) Let the work done by pipes $A, B$ and $C$ in $1 	ext{ h}$ be $\frac{1}{a}, \frac{1}{b}$ and $\frac{1}{c}$ respectively.Given:$\frac{1}{a} + \frac{1}{b} = \frac{1}{6}$$\frac{1}{b} + \frac{1}{c} = \frac{1}{10}$$\frac{1}{a} + \frac{1}{c} = \frac{1}{12}$Adding these three equations:$2 \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} ight) = \frac{1}{6} + \frac{1}{10} + \frac{1}{12}$$2 \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} ight) = \frac{10 + 6 + 5}{60} = \frac{21}{60} = \frac{7}{20}$Therefore,$\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = \frac{7}{40}$The time taken by $A, B$ and $C$ together to fill the tank is the reciprocal of the combined work rate:Time $= \frac{40}{7} 	ext{ h} = 5 \frac{5}{7} 	ext{ h}$.

$A, B$ and $C$ are three pipes connected to a tank. $A$ and $B$ together fill the tank in $6 \text{ h}$,$B$ and $C$ together fill the tank in $10 \text{ h}$ and $A$ and $C$ together fill the tank in $12 \text{ h}$. In how much time will $A, B$ and $C$ fill up the tank together?

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