A can do $$\frac{1}{3}$$ rd of a work in 5 days and B can do the do $$\frac{2}{5}$$ th of this work in 10 days. Both A and B, together can do the work in ?

A can do $$\frac{1}{3}$$ rd of a work in 5 days and B can do the do $$\frac{2}{5}$$ th of this work in 10 days. Both A and B, together can do the work in ? Correct Answer $${\text{9}}\frac{3}{8}{\text{ days}}$$

$$\eqalign{ & \frac{1}{3}{\text{work in 5 days}} \cr & {\text{then a complete work in}} \cr & = 5 \times 3 = 15{\text{ days}} \cr & {\text{B}} \to \frac{2}{5}{\text{work in 10 days}} \cr & {\text{then B completes work in}} \cr & = 10 \times \frac{5}{2} = {\text{25 days}} \cr} $$
L.C.M. of Total Work =75
One day work of A = $$\frac{{75}}{{15}}$$ = 5 unit/day
One day work of B = $$\frac{{75}}{{25}}$$ = 3 unit/day
$$\eqalign{ & \left( {{\text{A}} + {\text{B}}} \right){\text{ can do work}} \cr & = \frac{{75}}{8} = 9\frac{3}{8}{\text{ days}} \cr} $$