Question

$A$ and $B$ together can do a piece cf work in $12$ days, which $B$ and $C$ together can do in $16$ days. After $A$ has been working at it for $5$ days and $for7$ days, $C$ finishes it in $13$ days. In how many days $C$ alone will do the work $?$

• A. $16$
• B. $24$
• C. $36$
• D. $48$

Answer 1

Answer: (B)

$24$

Let the work done by $A$ in one day be $x$

work done by $B$ in one day be $y$

work done by $C$ in one day be $z$

$A$ and $B$ can do the work in $12$ days

$⟹$ work done by $A$ and $B$ in one day is $\frac{1}{12}$

$⟹x+y=\frac{1}{12}\cdots \left(1\right)$

$C$ and $B$ can do the work in $16$ days

$⟹$ work done by $C$ and $B$ in one day is $\frac{1}{16}$

$⟹z+y=\frac{1}{16}\cdots \left(2\right)$

$A$ has work for $5$ and $B$ for $7$ days,$C$ for $13$ days

$⟹5x+7y+13z=1\cdots \left(3\right)$

Solving $\left(1\right)$,$\left(2\right)$ and $\left(3\right)$

$x=\frac{1}{16},y=\frac{1}{48},z=\frac{1}{24}$

$⟹C$ alone can do the work in $24$ days