Five men working together can complete a work in 8 days. Om Prakash who can complete the same work independently in 24 days joined them after 4 days. Under the circumstances in how many days the work will be completed?

Given, 

5 men can complete the work in 8 days

Om Prakash can complete the work in 24 days

Let the total work = 24 unit (LCM of 8 and 24)

Efficiency = $$\frac{work}{time\ taken}$$

Efficiency of 5 men = $$\frac{24}{8}=3$$

Efficiency of Om Prakash = $$\frac{24}{24}=1$$

According to question, 

5 men worked 4 days 

i.e; work done in four days = $$3\times\ 4=12$$

Remaining work = 24 - 12 = 12 units

Now om prakash joined 

time = $$\frac{\left(remaining\ work\right)}{efficiency\ of\ working\ persons}$$

= $$\frac{12}{3+1}=3$$

So, total Days in completing work = 4 + 3 = 7 days

hence, Option C is correct.