Pipe A can fill a cistern in 6 , h and pipe B | vedclass

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(B) The rate of pipe $A$ is $\frac{1}{6}$ of the cistern per hour,and the rate of pipe $B$ is $\frac{1}{8}$ of the cistern per hour.Both pipes togethe

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$3 \frac{1}{3}$

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(B) The rate of pipe $A$ is $\frac{1}{6}$ of the cistern per hour,and the rate of pipe $B$ is $\frac{1}{8}$ of the cistern per hour.Both pipes together fill $\left(\frac{1}{6} + \frac{1}{8}ight) = \frac{4+3}{24} = \frac{7}{24}$ of the cistern per hour.In $2 \, h$,the part filled by both pipes is $2 	imes \frac{7}{24} = \frac{14}{24} = \frac{7}{12}$.The remaining part to be filled is $1 - \frac{7}{12} = \frac{5}{12}$.Pipe $B$ fills the remaining part at a rate of $\frac{1}{8}$ per hour.Time taken by $B$ to fill the remaining part $= \frac{5/12}{1/8} = \frac{5}{12} 	imes 8 = \frac{40}{12} = \frac{10}{3} = 3 \frac{1}{3} \, h$.

Pipe $A$ can fill a cistern in $6 \, h$ and pipe $B$ can fill it in $8 \, h$. Both the pipes are opened simultaneously,but after $2 \, h$ pipe $A$ is closed. How many hours will $B$ take to fill the remaining part of the cistern?

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