20 men can do a piece of work in 18 days. They worked together for 3 days, then 5 men joined. In how many days is the remaining work completed ?

Solution(By Examveda Team)

20 men → 18 days
⇒ Work done by 20 men working
Together = 1 work
⇒ Work done by them in 3 days working
Together = 1 × 3 = 3 work
⇒ Remaining work = 18 - 3 = 15 work
⇒ 15 work is to be done by (20 + 5) = 25 men
$$\eqalign{ & \therefore {\text{Efficiency of 1 man}} = \frac{1}{{20}} \cr & \Rightarrow {\text{Efficincy of 5 men}} \cr & = \frac{5}{{20}} \cr & = \frac{1}{4} \cr & \Rightarrow {\text{So, efficiency of }}\left( {20 + 5} \right) \cr & \Rightarrow 25{\text{ men}} = 1 + \frac{1}{4} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{5}{4}{\text{ working days}} \cr & {\text{Required time}} \cr & = \frac{{{\text{Work}}}}{{{\text{Efficiency}}}} \cr & = \frac{{15}}{{\frac{5}{4}}} \cr & = 12{\text{ days}} \cr} $$
Therefore, 12 more days will be taken to finish the remaining work

Alternate : 20 men can do 18 days
So, total work = 18 × 20 = 360
20 men 3 days work = 20 × 3 = 60
Remaining work = 360 - 60 = 300
After joining 5 men total men = 20 + 5 = 25
So, finish the remaining work in = $$\frac{{300}}{{25}} = 12{\text{ days}}$$