A contractor planned to complete a job in 9 days. He hired a certain number of men. However, 6 of them were absent from day one, and the remaining men finished the job in 15 days. How many men had the contractor originally planned to employ?
Correct Answer: 15
Introduction / Context:This question applies the person-days (or rate) method. If a contractor expects n men to finish in 9 days, the total work can be written as n * 9 in man-days. When only (n − 6) men actually work and the job takes 15 days, the same work is (n − 6) * 15 man-days. Equating these allows us to solve for n.
Given Data / Assumptions:
- Planned workforce = n men.
- Planned duration = 9 days.
- Actual workforce = n − 6 men (from day one).
- Actual duration = 15 days.
- Per-man productivity is constant throughout.
Concept / Approach:Total work is invariant. Express it both ways and solve for n. Using person-days avoids needing the per-man rate explicitly; it cancels out naturally.
Step-by-Step Solution:
Planned work = n * 9.Actual work = (n − 6) * 15.Equate: n * 9 = (n − 6) * 15.Expand: 9n = 15n − 90 ⇒ 6n = 90 ⇒ n = 15.Verification / Alternative check:If 15 men could finish in 9 days, but only 9 men (15 − 6) worked, the duration factor increases by 15/9 = 5/3; 9 * (5/3) = 15 days, consistent.
Why Other Options Are Wrong:6, 9, 12, 13 do not satisfy 9n = 15(n − 6); only n = 15 balances both sides.
Common Pitfalls:Confusing total work with rate; forgetting that fewer workers increase time proportionally; attempting to assign arbitrary per-man rates (unnecessary).
Final Answer:15