Question

$A$ can do a piece of work in $20$ days and $B$ in $40$ days. $A$ begins the work and there after they work alternately one on each day. On which day will the work be completed?

• A. $24$th day
• B. $25$th day
• C. $26$th day
• D. $27$th day

Answer 1

The correct option is D $27$th day

Work done by $(A+B)$ in 2 days $=\left(\frac{1}{20}+\frac{1}{40}\right)=\frac{3}{40}$

$\frac{3}{40}$ of the work is done by $(A+B)$ in 2 days

$\therefore$ Whole work is done by $(A+B)$ in $2\times \frac{40}{3}$ days $=\frac{80}{3}$ days $=26\frac{2}{3}$ days

$\therefore$ Work will be completed on 27th day.