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

Answer: Option C

$$\begin{array}{rl}& \frac{1}{3}\text{work in 5 days}\\ & \text{then a complete work in}\\ & =5\times 3=15\text{ days}\\ & \text{B}\to \frac{2}{5}\text{work in 10 days}\\ & \text{then B completes work in}\\ & =10\times \frac{5}{2}=\text{25 days}\end{array}$$
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
$$\begin{array}{rl}& \left(\text{A}+\text{B}\right)\text{ can do work}\\ & =\frac{75}{8}=9\frac{3}{8}\text{ days}\end{array}$$