Question

Hi,

I have a question about the following question. How many more employees have to be on team that will work on project A if the company wants to finish project within 72 days?


In the actual assignment, there was a table and you had to use the information from the table, so let me share the info from the table below (probably not all information is relevant for this question):


Project A Overview

No employees: 18

No of days: 95

Budgeted spend ($): 32000

Actual spend ($): 30000


Question: How many more employees have to be on team that will work on project A if the company wants to finish project within 72 days?


The answer suggested is: (18*95)/72 = 23.75 ( -> rounded ca. 24); 24 - 18 = 6 -> 6 employees have to join.


I really dont understand this logic. I dont understand why you can calculate 18 employees * 95 days if 95 days are the total project days.


I would have started like this:

No of days 95/ No of employees 18 = 5.27

5.27 * 72 days = 379.44


Difference:

379.44 - 18 = 361.44


I know the correct answer, which is 6 more employees, and even from a logical perspective, 361.44 looks way too big... they certainly dont need that many people. But I dont know how to calculate it to get 6 employees.


Could you please:

- Explain me this logic or

- Share an alternative calculation to derive to the correct answer?


Please help. Thank you so much.

Answer 1

6 workers have to be on the team to finish the project A in 72 days

Explanation:

Hi, I will help you with this question

In any project, if x employees work for y days to finish the project, then

Project = x y

x and y are variables but the project is constant, so

In the same job, if z employees work for m days to finish it, then

Project = z m

∵ Project = Project

∴ x y = z m

Very important note:

• This relation is called inverse variation, which means if the number of workers increases, then the number of days decreases

• The product of the 2 quantities (workers and the days) is constant

Let us use this rule in the question

∵ 18 workers will take 95 days to finish the project

∴ Project = 18 (95) = 1710

∵ x workers take 72 days to finish the same project

∴ Project = x (72)

→ Substitute the project by 1710

∴ 1710 = 72 x

Divide both sides by 72 to find x

∴ x = 23.75 ≈ 24

∵ x represents the number of workers

∴ 24 workers can finish the project in 72 days

∵ There are 18 workers already

∴ The number of workers needed = 24 - 18 = 6

∴ 6 workers have to be on the team to finish the project A in 72 days