A factory employs 600 men and 400 women. The average daily wage of all 1000 workers together is Rs. 25.50. Each woman receives Rs. 5 less per day than each man. What are the daily wages of a man and a woman respectively?

Introduction / Context:
This wages problem combines overall average income with a fixed difference between the wages of men and women. You know the counts of men and women, the average wage of all workers together, and that each woman receives Rs. 5 less than each man. The task is to determine the individual daily wages of a man and a woman. This is a typical linear equation and weighted average problem.

Given Data / Assumptions:
- Number of men = 600.
- Number of women = 400.
- Total workers = 600 + 400 = 1000.
- Average wage for all workers = Rs. 25.50 per day.
- Each woman receives Rs. 5 less than each man.
- Let the daily wage of a man be M rupees.
- Then the daily wage of a woman is M - 5 rupees.

Concept / Approach:
The total wage paid per day to all workers equals the overall average multiplied by the total number of workers. This same total can be expressed as wages paid to men plus wages paid to women. Writing the total in these two ways yields an equation in M that can be solved easily. Once M is found, the woman's wage is M - 5.

Step-by-Step Solution:
Step 1: Total wage per day for all workers based on the overall average = 25.50 * 1000 = Rs. 25500.Step 2: Total wage per day paid to men = 600 * M.Step 3: Total wage per day paid to women = 400 * (M - 5).Step 4: Combined total wage = 600M + 400(M - 5).Step 5: This combined total must equal Rs. 25500, so 600M + 400(M - 5) = 25500.Step 6: Expand the equation: 600M + 400M - 2000 = 25500.Step 7: Simplify: 1000M - 2000 = 25500.Step 8: Add 2000 to both sides: 1000M = 27500.Step 9: Therefore M = 27500 / 1000 = Rs. 27.50.Step 10: Wage of a woman = M - 5 = 27.50 - 5 = Rs. 22.50.

Verification / Alternative Check:
Check totals with these wages. Men: 600 * 27.50 = 16500. Women: 400 * 22.50 = 9000. Combined total = 16500 + 9000 = 25500. Dividing 25500 by 1000 workers gives an average of Rs. 25.50, which matches the given overall average. So the values are consistent with all data in the problem.

Why Other Options Are Wrong:
The other options either have the woman earning more than the man or do not preserve a difference of exactly Rs. 5. Substituting those pairs into the total wage calculation does not give a total of Rs. 25500, so they do not produce the required overall average of Rs. 25.50.

Common Pitfalls:
A typical mistake is to reverse the Rs. 5 difference, assuming that men earn less than women, or to forget to multiply by the correct number of workers in each group. Another error is to take a simple average of the two unknown wages instead of using weighted totals. Always base your calculation on total wage, not on a naive average of subgroups.

Final Answer:
The daily wage of a man is Rs. 27.50 and the daily wage of a woman is Rs. 22.50.