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 ?

Answer: Option A

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
$$\begin{array}{rl}& =\frac{\text{Work left}}{\text{Total work}}\\ & =\frac{25}{40}\\ & =\frac{5}{8}\end{array}$$