Question

A certain number of people were supposed to complete a work in 24 days. The work, however, took 32 days, since 9 people were absent throughout. How many people were supposed to be working originally ?

• A. 32
• B. 27
• C. 36
• D. 30

Answer 1

The Correct Option is C

To solve this problem, we use the concept of man-days, which states that the total work is equal to the number of people multiplied by the number of days they work.

Let the original number of people be x. They were supposed to complete the work in 24 days, so the total man-days required for the work is 24x.

However, since 9 people were absent, the number of people who actually worked is x - 9, and they took 32 days to complete the work.

Therefore, the total man-days worked in this scenario is 32(x - 9).

Setting these two expressions for total work equal, we have:

24x = 32(x - 9)

Expanding the equation, we get:

24x = 32x - 288

Rearrange the terms to solve for x:

24x - 32x = -288

-8x = -288

Dividing both sides by -8 gives:

x = 36

Thus, the original number of people supposed to work was 36.