Question

$A,B$ and $C$ are employed to do a piece of work for $Rs.529.$ $A$ and $B$ together are supposed to do $\frac{19}{23}$ of the work and $B$ and $C$ together $\frac{8}{23}$ of the work. What amount should $A$ be paid ?

Answer 1

$A,B$ together does $\frac{19}{23}$ of the work

$⟹A+B=\frac{19}{23}\cdots \left(1\right)$

$B,C$ together does $\frac{8}{23}$ of the work

$⟹B+C=\frac{8}{23}\cdots \left(2\right)$

All together they work as a whole

$⟹A+B+C=1\cdots \left(3\right)$

From $\left(1\right),\left(2\right),\left(3\right)$

$⟹B=\frac{5}{23}$

put it in $\left(1\right)$

$⟹A=\frac{14}{23}$

$A$`s payment $=\frac{14}{23}\times 529=14\times 23=322$