In a shopping complex, 5 men or 8 women do an equal amount of work in a day. A…
2025
In a shopping complex, 5 men or 8 women do an equal amount of work in a day. A job requires 3 men and 5 women to finish the job in 10 days. How many women are required to finish the same job in 14 days?
- A.
8
- B.
7
- C.
6
- D.
9
Show answer & explanation
Correct answer: B
Concept: In equivalence-based work problems, when a rate relation between two types of workers is given (e.g., 5 men = 8 women in a day's output), convert every worker into one common unit before combining anything. Total work then stays fixed: workers x days is constant, expressed in that common unit-day (here, woman-days).
Application:
From 5 men = 8 women (one day's output), 1 man = 8/5 women -- a man's daily work equals 8/5 of a woman's.
Convert the original team's men into women-equivalents: 3 men = 3 x 8/5 = 24/5 = 4.8 women. Adding the 5 women already on the team gives 4.8 + 5 = 9.8 women-equivalent workers.
Total work for the job = 9.8 women x 10 days = 98 woman-days -- this total effort is fixed, however the team is later composed.
For a team of all women finishing in 14 days: women required = total work / days = 98 / 14 = 7 women.
Cross-check: 7 women working 14 days give 7 x 14 = 98 woman-days -- exactly matching the original team's 98 woman-days, confirming the total effort is unchanged and only the days-per-worker trade-off differs.