16 men can finish a work in 24 days and 48 boys can finish the same work in 16 days. 12 men started the work and after 4 days 12 boys joined them. In how many days can they finish the remaining work ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{1 men's 1 day's work}} \cr & = \frac{1}{{24 \times 16}} \cr & = \frac{1}{{384}} \cr & {\text{1 boy's 1 day's work}} \cr & = \frac{1}{{16 \times 48}} \cr & = \frac{1}{{768}} \cr & {\text{12 men's 4 day's work}} \cr & = \left( {\frac{{12}}{{384}} \times 4} \right) \cr & = \frac{1}{8} \cr & {\text{Remaining work}} \cr & = \left( {1 - \frac{1}{8}} \right) \cr & = \frac{7}{8} \cr & \left( {{\text{12 men}} + {\text{12 boy}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{{12}}{{384}} + \frac{{12}}{{768}}} \right) \cr & = \left( {\frac{1}{{32}} + \frac{1}{{64}}} \right) \cr & = \frac{3}{{64}} \cr} $$
$$\frac{3}{{64}}$$ work is done by (12 men + 12 boy)'s in 1 day
$$\eqalign{ & \therefore \frac{7}{8}{\text{ work is done by them in }} \cr & {\text{ = }}\frac{{64}}{3} \times \frac{7}{8}{\text{ days}} \cr & = \frac{{56}}{3}{\text{ days}} \cr & = {\text{18}}\frac{2}{3}{\text{ days}} \cr} $$