Question

$A$ and $B$ can do a piece of work in $10$ days. $B$ and $C$ can do it in $12$ days. $A$ and $C$ can do it in $15$ days. How long will $A$ take to do it alone?

Answer 1

${(A+B)}^{\prime }s$, $1$ day's work$=\frac{1}{10}$

${(B+C)}^{\prime }s$, $1$ day's work$=\frac{1}{12}$

${(C+A)}^{\prime }s$, $1$ day's work$=\frac{1}{15}$

On adding,

$2{(A+B+C)}^{\prime }s$, $1$ day's work$=\frac{1}{10}+\frac{1}{12}+\frac{1}{15}$

$=\frac{6+5+4}{60}=\frac{1}{4}$

$\therefore {(A+B+C)}^{\prime }s$, $1$ day's work$=\frac{1}{8}$

$\therefore A^{\prime }s$, $1$ day's work$=\frac{1}{8}-\frac{1}{12}=\frac{3-2}{24}=\frac{1}{24}$

$\therefore A$ alone will complete the work in $24$ days.