A can complete 1/3 of a work in 5 days and B, 2/5 of the work in 10 days. In how many days both A and B together can complete the work ?

Answer: Option C

Whole work will be done by A in
$$\begin{array}{rl}& =\left(5\times 3\right)\\ & =15\text{ days}\end{array}$$
Whole work will be done by B in
$$\begin{array}{rl}& =\left(10\times \frac{5}{2}\right)\\ & =25\text{ days}\end{array}$$
$$\begin{array}{rl}& \text{A’s 1 day’s work}=\frac{1}{15}\\ & \text{B’s 1 day’s work}=\frac{1}{25}\\ & \left(\text{A}+\text{B}\right)\text{’s 1 day’s work}\\ & \text{ = }\left(\frac{1}{15}+\frac{1}{25}\right)\\ & =\frac{16}{150}\\ & =\frac{8}{75}\end{array}$$
∴ A and B together can complete the work in
$$\begin{array}{rl}& =\frac{75}{8}\\ & =9\frac{3}{8}\text{days}\text{.}\end{array}$$