40 men can complete a piece of work in 15 days. 20 more men joined them after 5 days they start doing work. How many days will be required by them to finish the remaining work ?

Solution(By Examveda Team)

Work done by 40 men in 5 days = $$\frac{1}{3}$$
(As if whole work is completed in 15 days then in 5 days $${{{\frac{1}{3}}^{{\text{rd}}}}}$$ of the work will be finished)
$$\eqalign{ & {\text{Remaining work}} = 1 - \frac{1}{3} = \frac{2}{3} \cr & \because 40{\text{ men do 1 work in 15 days}}{\text{.}} \cr & {\text{60 men can do }}\frac{2}{3}{\text{work in }}x{\text{ day}} \cr & \frac{{{{\text{M}}_1}{{\text{D}}_1}}}{{{{\text{W}}_1}}}{\text{ = }}\frac{{{{\text{M}}_2}{{\text{D}}_2}}}{{{{\text{W}}_2}}} \cr & {{\text{M}}_1} = 40{\text{ , }}{{\text{M}}_2} = 60 \cr & {{\text{D}}_1} = 15{\text{ , }}{{\text{D}}_2} = x \cr & {{\text{W}}_1} = 1{\text{ ,}}{{\text{W}}_2} = \frac{2}{3} \cr & \Rightarrow \frac{{40 \times 15}}{1} = \frac{{60 \times x}}{2} \cr & \Rightarrow \frac{2}{3}\left( {40 \times 15} \right) = 60x \cr & \Rightarrow 2 \times 40 \times 5 = 60x \cr & \Rightarrow x = \frac{{20}}{3} \cr & \Rightarrow x = 6\frac{2}{3}{\text{ days}} \cr} $$