#### Question

150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.

#### Solution

Let *x* be the number of days in which 150 workers finish the work.

According to the given information,

150*x* = 150 + 146 + 142 + …. (*x* + 8) terms

The series 150 + 146 + 142 + …. (*x* + 8) terms is an A.P. with first term 150, common difference –4 and number of terms as (*x* + 8)

However, *x* cannot be negative.

∴*x* = 17

Therefore, originally, the number of days in which the work was completed is 17.

Thus, required number of days = (17 + 8) = 25

Is there an error in this question or solution?

Solution 150 Workers Were Engaged to Finish a Job in a Certain Number of Days. 4 Workers Dropped Out on Second Day, 4 More Workers Dropped Out on Third Day and So On. It Took 8 More Days to Finish the Work. Find the Number of Days in Which the Work Was Completed. Concept: Concept of Series.