Question

$A$ and $B$ can do a work in 8 days. $B$ and $C$ together in 6 days while $C$ and $A$ together in 10 days. If they all work together, in The work will be completed in $\frac{k}{17}$ days, where $k$ is

Answer 1

Given that:

$(A+B{)}^{\prime }sonedaywork=\frac{1}{8}$ ......(1)

$(B+C{)}^{\prime }sonedaywork=\frac{1}{6}$ ......(2)

$(A+C{)}^{\prime }sonedaywork=\frac{1}{10}$ ......(3)

On adding all the above equations, we get

$2(A+B+C{)}^{\prime }sonedaywork=\frac{1}{8}+\frac{1}{6}+\frac{1}{10},$

$2(A+B+C{)}^{\prime }sonedaywork=\frac{15+20+12}{120},$

$(A+B+C{)}^{\prime }sonedaywork=\frac{47}{2\times 120},$

$(A+B+C{)}^{\prime }sonedaywork=\frac{47}{240}.$

Hence, $A,B,C$ will complete the work together in $\frac{240}{47}$ days.