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

Hint:

Total work (people times days) stays constant; equate 24 times the original people to 32 times the people who actually worked.

Answer 1

The Correct Option is C

Since the total amount of work does not change, the number of people needed is inversely proportional to the number of days taken.

1. Set up the inverse proportion. If $x$ is the original number of people (planned for 24 days) and $x - 9$ people actually worked for 32 days, then $\dfrac{x}{x-9} = \dfrac{32}{24} = \dfrac{4}{3}$.
2. Cross-multiply. $3x = 4(x - 9) = 4x - 36$.
3. Solve for $x$. $3x - 4x = -36 \Rightarrow -x = -36 \Rightarrow x = 36$.
4. Verify. $24 \times 36 = 864$ man-days, and $32 \times (36 - 9) = 32 \times 27 = 864$ man-days. Both match.

So 36 people were originally supposed to work, option C.