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 ?

Answer: Option D

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)
$$\begin{array}{rl}& \text{Remaining work}=1-\frac{1}{3}=\frac{2}{3}\\ & \because 40\text{ men do 1 work in 15 days}\text{.}\\ & \text{60 men can do }\frac{2}{3}\text{work in }x\text{ day}\\ & \frac{{\text{M}}_1{\text{D}}_1}{{\text{W}}_1}\text{ = }\frac{{\text{M}}_2{\text{D}}_2}{{\text{W}}_2}\\ & {\text{M}}_1=40\text{ , }{\text{M}}_2=60\\ & {\text{D}}_1=15\text{ , }{\text{D}}_2=x\\ & {\text{W}}_1=1\text{ ,}{\text{W}}_2=\frac{2}{3}\\ & \Rightarrow \frac{40\times 15}{1}=\frac{60\times x}{2}\\ & \Rightarrow \frac{2}{3}\left(40\times 15\right)=60x\\ & \Rightarrow 2\times 40\times 5=60x\\ & \Rightarrow x=\frac{20}{3}\\ & \Rightarrow x=6\frac{2}{3}\text{ days}\end{array}$$