Question

Elan Musk need some workers to complete the project for his organisation Tesla, he hired 150 workers to finish that in a certain number of days. Because of food poisoning four workers dropped the second day, then because of Dengue four more workers were unable to come on the next day and so on. Just because of these situations the project work delayed for 8 more days. Calculate the time period (in days) in which the project was completed.
1. 25 days
2. 27 days
3. 29 days
4. 31 days

Answer 1

Correct Answer - Option 1 : 25 days

Given∶

150 workers were hired to complete the project 2nd day because of food poisoning 4 workers were dropped.

Next day because of Dengue 4 more workers were absent.

Formula Used∶

Sum of n terms of a A.P. = n/2[2a + (n - 1)d]

Factorization of quadratic equation.

Calculation∶

Suppose the work is completed in n days when the workers started dropping. Since 4 workers are dropped on every day expect the first day. Therefore, the total number of workers who worked all the n days is the sum of n terms of n A.P. with first term 150 and common difference - 4

n/2{2 × 150 + (n - 1) × - 4} = n(152 - 2n)

Had the workers not dropped then the project would have finished in (n-8) days with 150 workers working on each day. Therefore, the total number of workers who would have worked all the n days in 150(n-8).

n(152 - 2n) = 150(n - 8) 

⇒ n² - n - 600 = 0

⇒ (n - 25)(n + 24) = 0

⇒ n = 25.

Thus, the work is completed in 25 days.