Question

A tank is filled in 1 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe B alone take to fill the tank?

Answer 1

$\sf\red{\underline{\underline{Answer:}}}$

$\sf{The \ pipe \ B \ alone \ can \ fill \ the \ tank}$

$\sf{in \ 3 \ hours \ 30 \ minutes.}$

$\sf\orange{Given:}$

$\sf{\implies{A \ tank \ is \ filled \ in \ 1 \ hour \ by}}$

$\sf{three \ pipes \ A, \ B \ and \ C.}$

$\sf{\implies{Speed_{pipe \ C}=2\times \ Speed_{pipe \ B}}}$

$\sf{\implies{Speed_{pipe \ B}=2\times \ Speed_{pipe \ A}}}$

$\sf\pink{To \ find:}$

$\sf{How \ much \ time \ will \ pipe \ B \ alone}$

$\sf{take \ to \ fill \ the \ tank.}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{Let \ pipe \ B \ take \ 2x \ hours \ to \ fill \ the \ tank.}$

$\sf{\therefore{Pipe \ C \ will \ take \ x \ hours}}$

$\sf{and \ pipe \ A \ will \ take \ 4x \ hours.}$

$\sf{According \ to \ the \ given \ condition.}$

$\sf{\frac{1}{2x}+\frac{1}{x}+\frac{1}{4x}=\frac{1}{1}}$

$\sf{\therefore{\frac{2+4+1}{4x}=1}}$

$\sf{\therefore{\frac{7}{4x}=1}}$

$\sf{\therefore{2x=\frac{7}{2}}}$

$\sf{\therefore{2x=3.5 \ hr}}$

$\sf{3.5 \ hr=3 \ hours \ and \ 30 \ minutes.}$

$\sf\purple{\tt{\therefore{The \ pipe \ B \ alone \ can \ fill \ the \ tank}}}$

$\sf\purple{\tt{in \ 3 \ hours \ 30 \ minutes.}}$