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

Solution(By Examveda Team)

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