Question

$A$ can do a piece of work in $4$ hours; $B$ and $C$ together can do it in $3$ hours, while $A$ and $C$ together can do it in $2$ hours. How long will $B$ alone take to do it?

• A. $8$ hours
• B. $10$ hours
• C. $12$ hours
• D. $24$ hours

Answer 1

The correct option is C $12$ hours

$A^{\prime }s1$hour's work $=\frac{1}{4}$

${(B+C)}^{\prime }s1$hour's work $=\frac{1}{3}$

${(A+C)}^{\prime }s1$hour's work $=\frac{1}{2}$

${(A+B+C)}^{\prime }s1$hour's work $=\frac{1}{4}+\frac{1}{3}=\frac{7}{12}$

$B^{\prime }s1$hour's work $=\frac{7}{12}-\frac{1}{2}=\frac{1}{12}$

$\therefore B$ along will take $12$ hours to do the work.