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

Introduction / Context:
This question combines average wage, total workers, and a fixed difference between the wages of two groups. It is a standard application of the weighted average concept and linear equations. You must express the total wage paid to all workers in terms of the unknown man's wage and then use the given overall average to solve for that unknown.

Given Data / Assumptions:

• Total workers = 600 men + 400 women = 1000 workers.
• Average wage of all workers together = Rs 25.50 per day.
• Each woman earns Rs 5 less per day than each man.
• We need to find the daily wage of a man and that of a woman.

Concept / Approach:
Let the daily wage of a man be m rupees. Then the daily wage of a woman is (m - 5) rupees. Using the average wage information, we know that the total daily wage bill equals (average wage) * (number of workers) = 25.5 * 1000. We also know that this total wage is the sum of wages paid to men plus the sum of wages paid to women. This gives an equation in terms of m that we can solve directly.

Step-by-Step Solution:
Let the daily wage of each man be m rupees.Then the daily wage of each woman is m - 5 rupees.Total daily wage paid to all workers = average wage * number of workers = 25.5 * 1000 = Rs 25500.Total wage paid to 600 men = 600 * m.Total wage paid to 400 women = 400 * (m - 5).So, 600m + 400(m - 5) = 25500.Simplify: 600m + 400m - 2000 = 25500, so 1000m - 2000 = 25500.Therefore, 1000m = 27500, and m = 27.5.Thus, the daily wage of a man is Rs 27.50 and that of a woman is m - 5 = 22.5 rupees.

Verification / Alternative check:
Check using totals: wage of a man = Rs 27.50, wage of a woman = Rs 22.50. Total wage to men = 600 * 27.5 = Rs 16500. Total wage to women = 400 * 22.5 = Rs 9000. Combined total = 16500 + 9000 = Rs 25500. Average wage = 25500 / 1000 = Rs 25.50, which matches the given average. Therefore, the solution is consistent.

Why Other Options Are Wrong:
Option a reverses the relationship and gives a woman more pay than a man, contradicting the statement that a woman earns Rs 5 less. Options c and d also do not preserve the fixed difference of Rs 5 in the correct direction or fail to produce an overall average of Rs 25.50 when weighted by 600 men and 400 women. Option e is arbitrarily large and does not satisfy the total wage and average constraints. Only option b matches all the conditions.

Common Pitfalls:
Errors can come from mixing up the direction of the Rs 5 difference or forgetting that there are 1000 workers, not 600 or 400 only. Some students also mistakenly average the two group wages without weighting them by their respective counts. Always set up the total wage equation carefully and solve step by step.

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