Question

$A,B$ and $C$ can finish a job working alone in $72,24$ and $36$ days respectively. In how many days they can finish the job if they worked together?

• A. $12$
• B. $9$
• C. $15$
• D. $18$

Answer 1

The correct option is A $12$

Let the total work be $72$ units (LCM on $72,24$ and $36$).

$A,B$ and $C^{\prime }s$ one day work is $1,3$ and $2$ units respectively.

Required number of days $=\frac{72}{6}=12$.

Alternate method

$(A+B+C{)}^{\prime }s$ one day work =$\frac{1}{72}+\frac{1}{24}+\frac{1}{36}$

$=\frac{1+2+3}{72}=\frac{6}{72}$

Number of days required $=\frac{72}{6}=12$ days to finish the work when 3 of them work together.