A can do a piece of work in 20 days and B in 40 days. If they work together for 5 days, then the fraction of the work that is left is ?

A. $$\frac{5}{8}$$

B. $$\frac{8}{{15}}$$

C. $$\frac{7}{{15}}$$

D. $$\frac{1}{{10}}$$

Answer: Option A

Solution(By Examveda Team)

L.C.M of total work = 40
One day work of A = $$\frac{{40}}{{20}}$$ = 2 unit/day
One day work of B = $$\frac{{40}}{{40}}$$ = 1 unit/day
(A + B)'s one day work is (2 + 1) units
(A + B)'s 5 day work is 3 × 5 = 15 units
Work left = 40 - 15 = 25
∴ Fraction of work left
$$\eqalign{ & = \frac{{{\text{Work left}}}}{{{\text{Total work}}}} \cr & = \frac{{25}}{{40}} \cr & = \frac{5}{8} \cr} $$