X alone can complete a piece of work in 40 days. He worked for 8 days and left. Y alone completed the remaining work in 16 days. How long would X and Y together take to complete the work ?

A. $$13\frac{1}{3}\,{\text{days}}$$

B. $${\text{14 days}}$$

C. $${\text{15 days}}$$

D. $$16\frac{2}{3}\,{\text{days}}$$

Answer: Option A

Solution(By Examveda Team)

Let total work = 40 units
$$\eqalign{ & {\text{X's 1 day work}} = 1{\text{ unit}} \cr & {\text{X's 8 days work is}} \cr & = 8 \times 1 \cr & = 8{\text{ units}} \cr & {\text{Work left}} = 40 - 8 = 32 \cr & {\text{Y's 1 day work}} = 2{\text{ unit}} \cr & {\text{X's 8 days work is}} = 1{\text{ units}} \cr} $$
X + Y complete the whole work together in
$$\eqalign{ & = \frac{{40}}{{2 + 1}} \cr & = 13\frac{1}{3}\,{\text{days}} \cr} $$