Determining men and women daily wages first: 4 men and 6 women earn ₹ 1600 in 5 days; 3 men and 7 women earn ₹ 1740 in 6 days. In how many days will 7 men and 6 women earn ₹ 3760?

Introduction / Context:
We first extract the per-day earnings equations for men and women using the two scenarios. With those unit wages known, we can compute the daily earnings of the new team and then determine how many days are required to reach ₹ 3760.

Given Data / Assumptions:

• (4m + 6w) for 5 days = ₹ 1600 ⇒ per day = 1600/5 = 320
• (3m + 7w) for 6 days = ₹ 1740 ⇒ per day = 1740/6 = 290
• Find days d for (7m + 6w) to earn ₹ 3760

Concept / Approach:
Let M and W be daily wages of a man and a woman. Solve 4M + 6W = 320 and 3M + 7W = 290. Then compute per-day for (7M + 6W) and divide 3760 by that to get the time required.

Step-by-Step Solution:
4M + 6W = 3203M + 7W = 290Solving ⇒ M = 50, W = 20Daily for 7 men + 6 women = 7*50 + 6*20 = 350 + 120 = ₹ 470Days d = 3760 / 470 = 8

Verification / Alternative check:
Back-substitute M, W into both original equations to verify correctness before using them for the final calculation — both equalities hold.

Why Other Options Are Wrong:
6, 10, 12 days correspond to daily totals not equal to ₹ 470; they do not reach ₹ 3760 exactly.

Common Pitfalls:
Arithmetic slips in solving the two-variable system; forgetting to convert totals to per-day values; mixing up rates and wages.

Final Answer:
8 days