Men–women wage conversion: The wages of 10 women for 5 days total ₹ 1250. The daily wage of a man is twice that of a woman. How many men must work for 8 days to collectively earn ₹ 1600?

Introduction / Context:
This problem converts between women's and men's wage rates and then scales the workforce to meet a target earning in a given time. The essential tools are unit wage calculation and proportional reasoning.

Given Data / Assumptions:

• Total wages for 10 women over 5 days = ₹ 1250
• Therefore, 1 woman per day wage = ?
• 1 man per day wage = 2 * (1 woman per day wage)
• Target: men working 8 days must earn ₹ 1600

Concept / Approach:
First find the daily wage of a woman, then double it to get the man's daily wage. Finally, compute how many men are needed so that their combined 8-day wage equals ₹ 1600.

Step-by-Step Solution:
Let w = woman's daily wage10 women for 5 days ⇒ 50w = 1250 ⇒ w = ₹ 25Man's daily wage m = 2w = ₹ 50Let n = number of men. Total in 8 days = n * 8 * 50 = 400n400n = 1600 ⇒ n = 4

Verification / Alternative check:
4 men for 8 days earn 4 * 8 * 50 = ₹ 1600, matching the requirement.

Why Other Options Are Wrong:
5, 6, or 7 men would overshoot the target earnings; fewer than 4 would undershoot.

Common Pitfalls:
Using 10 instead of 50 woman-days in the initial calculation; forgetting to multiply by the number of days when converting to men's wages.

Final Answer:
4