Question

$A,B$ and $C$ can do a job in $11,20$ and $55$ days respectively. How soon can the work be done if $A$ is assisted by $B$ and $C$ on alternate days?

• A. $7$ days
• B. $9$ days
• C. $8$ days
• D. $10$ days

Answer 1

The correct option is C $8$ days

$(A+B{)}^{\prime }s$ 1 days work$=(\frac{1}{11}+\frac{1}{20})$$=\frac{31}{220}$.
$(A+C{)}^{\prime }s$ 1 days work$=(\frac{1}{11}+\frac{1}{55})$$=\frac{6}{55}$.
Work done in 2 days$=(\frac{31}{220}+\frac{6}{55})$$=\frac{55}{220}$ $=\frac{1}{4}$
Now, $\frac{1}{4}$ work is done in $2$ days.
$\therefore$ Whole work will be done in $(2\times 4)=8$ days.