Mixed-team productivity then women-only completion Twenty-five men and fifteen women can complete a job in 12 days. All begin together; after 8 days the women stop. The remaining work is finished by 25 men in 6 days. How long would it take if only 15 women worked from start to finish?

Difficulty: Medium

Correct Answer: None of these

Explanation:


Introduction / Context:
This is a two-phase workforce problem used to infer relative productivities of men and women. After learning the ratio, compute the total work in man-rate units and then find the women-only duration.



Given Data / Assumptions:

  • Phase 1: (25 men + 15 women) for 8 days, then women leave.
  • Phase 2: 25 men alone finish the remainder in 6 days.
  • Productivity is linear and constant.


Concept / Approach:
Let man rate = m and woman rate = w (jobs per day). Equate Phase-2 remainder to solve for w in terms of m, then compute total job in m-units and divide by 15w.



Step-by-Step Solution:

Work done in first 8 days = (25m + 15w)*8Remaining work = total W − (25m + 15w)*8Given: 25m * 6 = remaining ⇒ 150m = W − 8(25m + 15w)Also, W = (25m + 15w)*12 (from the 12-day completion by the mixed team)Substitute: 150m = (25m + 15w)*12 − 8(25m + 15w) = 4(25m + 15w)150m = 100m + 60w ⇒ 50m = 60w ⇒ m/w = 6/5 ⇒ w = (5/6)mTotal work W in m-units = (25m + 15*(5/6)m)*12 = (25m + 12.5m)*12 = 450mWomen-only daily rate (15 women) = 15w = 15*(5/6)m = 12.5mTime with 15 women alone = 450m / 12.5m = 36 days


Verification / Alternative check:
36 days is consistent with the inferred m:w ratio 6:5 and total job size 450m.



Why Other Options Are Wrong:
60, 88, 94 do not match the derived 36 days. Hence the correct choice within the given set is “None of these.”



Common Pitfalls:
Assuming the total work is 12 days of the mixed team without converting to rates; or forgetting to scale by 15w for the women-only case.



Final Answer:
None of these

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