Six men or ten women can reap a field in 15 days. How many days will it take for a team of 12 men and 5 women to reap the same field?

Introduction / Context:
This is a classic work-rate comparison. We convert all workers to a common efficiency unit (e.g., woman equivalents) using given equivalences and then compute the time for a mixed team.

Given Data / Assumptions:

• 6 men can finish in 15 days.
• 10 women can finish in 15 days.
• Goal: time for 12 men and 5 women working together.

Concept / Approach:
Total work W is the same. With 10 women finishing in 15 days, W = 10w * 15 (where w = one woman's daily work). With 6 men finishing in 15 days, W = 6m * 15 (m = one man's daily work). Equating gives a relation between m and w, then find the mixed team's rate and compute days = W / rate.

Step-by-Step Solution:
From 6 men in 15 days: W = 6m * 15 = 90m. From 10 women in 15 days: W = 10w * 15 = 150w. Equate 90m = 150w ⇒ m = (150/90)w = (5/3)w. Mixed team daily rate = 12m + 5w = 12*(5/3)w + 5w = 20w + 5w = 25w. Total work W = 150w. Days = W / rate = 150w / 25w = 6 days.

Verification / Alternative check:
Using man-units: m = (5/3)w ⇒ 12 men = 12*(5/3)w = 20w; add 5w = 25w as above. Correct consistency.

Why Other Options Are Wrong:
5, 8, 9, 12 days do not match the computed ratio-based result from the given equivalence; only 6 days fits the combined rate calculation.

Common Pitfalls:
Averaging days directly instead of converting to rates, or forgetting to convert all workers to a common unit before adding rates.

Final Answer:
6 days