Question

A and B can together finish a work in $30$ days. They worked together for $20$ days and then B left. After another $20$ days A finished the remaining work. The number of days in which B alone can finish the work is

• A. $50$
• B. $48$
• C. $54$
• D. $60$

Answer 1

The correct option is D $60$

: Let the total unit of work be $60$ units. [LCM of $20$ and $30$]

(A + B) do = $\frac{60}{30}$ = $2$ units/day
(A + B)'s $20$ days work = 2$\times$ $20$
= $40$ units
Work left = $60$-$40$ = $20$ units.
To complete $20$ units of work, A took $20$ days.
$\therefore$ As per day work = $\frac{20}{20}$ = $1$ unit/day
B's per day work =$2-1$ = $1$ unit/day.

Hence B would require 60 days to finish the work.