A certain company employed 400 men and 600 women and the average wage was Rs.…

When a combined group is split into two sub-groups of sizes n1 and n2 with individual means x1 and x2, the weighted average of the whole group is (n1 x1 + n2 x2) / (n1 + n2). When one mean is expressed as an offset of the other (here, a woman's wage is Rs. 4 less than a man's), that offset is substituted into the weighted-average equation to leave a single unknown.

Let the man's daily wage be M. Since a woman earns Rs. 4 less than a man, the woman's daily wage is (M - 4). There are 400 men and 600 women, so 1000 employees in total, and the overall average wage is Rs. 22.60.

1. Write the weighted-average equation: (400 × M + 600 × (M - 4)) / 1000 = 22.60

2. Multiply both sides by 1000: 400M + 600(M - 4) = 22600

3. Expand the bracket: 400M + 600M - 2400 = 22600

4. Combine like terms: 1000M - 2400 = 22600

5. Add 2400 to both sides: 1000M = 25000

6. Divide both sides by 1000: M = 25, so the woman's wage = M - 4 = 21

The man's daily wage is Rs. 25 and the woman's daily wage is Rs. 21.

Substituting back, (400 × 25 + 600 × 21) / 1000 = (10000 + 12600) / 1000 = 22600 / 1000 = Rs. 22.60, matching the given average, and 25 - 21 = 4, matching the given wage gap - both conditions are independently confirmed.