10 Men begin to work together on a job, but after some days, 4 of them leave the job. As a result the job which could have been completed in 40 days is completed in 50 days. How many days after the commencement of the work did the 4 men leave?
A. 25
B. 30
C. 10
D. 15

Hint: Let the no. of days after which the 4 men left is x. 10 men finish the work in 40 days whereas after 4 men leaving the work gets finished in 50 days. After x days, the no. of days left for 10 men is $ 40 - x $ ; no. of days left for 6 men is . 10 men can finish some work in $ 40 - x $ days whereas 6 men can finish the same work in $ 50 - x $ days. So equate these two to get the value of x.

Complete step-by-step answer:
We are given that 10 Men begin to work together on a job, but after some days, 4 of them leave the job. As a result the job which could have been completed in 40 days is completed in 50 days..
We have to find after how many days the 4 men left.
For 10 men, it takes 40 days. But after some x days 4 men left and the remaining men finished the whole work in 50 days. So after x days, the work done by 10 men in $ 40 - x $ days is equal to work done by 6 men in $ 50 - x $ days.
This means that $ 10\left( {40 - x} \right) = 6\left( {50 - x} \right) $
Expanding the above equation, we get $ 400 - 10x = 300 - 6x $
Putting the terms containing x one side and the constant terms one side, we get $ 6x - 10x = 300 - 400 $
 $ \Rightarrow - 4x = - 100 $
 $ \therefore x = \dfrac{{100}}{4} = 25 $
Therefore, after 25 days the 4 men left the work, which means 10 men worked for 25 days and the remaining 6 men after 4 left worked for another $ 25\; days $ .
So, the correct answer is “Option A”.

Note: While solving a linear equation, always put the terms containing variables on the left hand side, as the process gets easier. We can also solve this question by finding the work rate of one man. 10 men can finish the work in 40 days, which means one man can finish the total work in 400 days. So from this we can find the work rate of one man and solve it.