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 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?
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Total work (people times days) stays constant; equate 24 times the original people to 32 times the people who actually worked.
Updated On: Jul 16, 2026
- 32
- 27
- 36
- 30
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Express the total work in two ways.
Let the number of people originally supposed to work be \(x\). The total work (in man-days) is fixed, so it equals people multiplied by days in both scenarios. Originally: work \(= 24x\) man-days. Actually, only \(x - 9\) people worked (since 9 were absent throughout), and it took 32 days, so work \(= 32(x - 9)\) man-days.
Step 2: Equate the two expressions and solve.
\[ 24x = 32(x - 9) \] Dividing both sides by 8: \[ 3x = 4(x - 9) = 4x - 36 \] \[ 36 = 4x - 3x = x \] So \(x = 36\).
Final Answer:
36 people were originally supposed to work on this job. \[ \boxed{x = 36} \]
Let the number of people originally supposed to work be \(x\). The total work (in man-days) is fixed, so it equals people multiplied by days in both scenarios. Originally: work \(= 24x\) man-days. Actually, only \(x - 9\) people worked (since 9 were absent throughout), and it took 32 days, so work \(= 32(x - 9)\) man-days.
Step 2: Equate the two expressions and solve.
\[ 24x = 32(x - 9) \] Dividing both sides by 8: \[ 3x = 4(x - 9) = 4x - 36 \] \[ 36 = 4x - 3x = x \] So \(x = 36\).
Final Answer:
36 people were originally supposed to work on this job. \[ \boxed{x = 36} \]
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