A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in

A. 5 days

B. 6 days

C. 9 days

D. 10 days

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Solution(By Apex Team)

Answer: Option B Let the total unit of work be 6 units (LCM of 2 and 3) $(\mathrm{A}+\mathrm{B}) \mathrm{do}=\frac{6}{3}=2 \mathrm{units} / \mathrm{day}$ $(\mathrm{A}+\mathrm{B})^{\prime} \mathrm{s} 2 \text { day work }=2 \times 2=4 \text { units }$ $\text { Work left }=6-4=2 \text { units }$ This remaining work is done by A in 2 days. $\therefore \text { A’s per day work }=\frac{2}{2}=1 \text { unit/day }$ $\therefore \text { B’s per unit work }=(\mathrm{A}+\mathrm{B})^{\prime} \mathrm{s} \text { work }-\mathrm{A}^{\prime} \mathrm{s} \text { work }$ $=2-1=1 \text { unit/day }$ $\text { B alone can complete the work in }$ $=\frac{6}{1}=6 \text { days. }$