A certain factory employed 600 men and 400 women and the average wage was ₹ 25.50 per day. If a woman got ₹ 5 less than a man, then what are their daily wages?

### Concept & Logic This relies on the principle of the weighted average. The total wages paid to the entire workforce is simply the sum of wages paid to all men plus the sum of wages paid to all women. ### Step-by-Step Solution * **Given Information:** Total men = $600$ Total women = $400$ Total workforce = $1000$ Overall average wage = ₹ $25.50$ * Let the daily wage of a man be $M$. Let the daily wage of a woman be $W$. We are given that $W = M - 5$. * **Calculation:** Total daily wage of the factory = $1000 \times 25.50 = 25500$. Set up the equation for total wages: $$600M + 400W = 25500$$ Substitute $W$ with $(M - 5)$: $$600M + 400(M - 5) = 25500$$ $$600M + 400M - 2000 = 25500$$ $$1000M = 27500$$ $$M = 27.50$$ Now, find the woman's wage: $$W = 27.50 - 5 = 22.50$$ ### Exam Strategy & Shortcut Use the method of deviations or "assume a base". Assume all $1000$ workers were paid the woman's lower wage, $W$. The $600$ men get an "extra" ₹ $5$ each, creating a total surplus of $600 \times 5 = 3000$. If we distribute this surplus evenly over all $1000$ workers, it increases the overall average by $3000 / 1000 = 3$. So, Average Wage = $W + 3$. We know Average Wage = $25.50$. $W + 3 = 25.50 \Rightarrow W = 22.50$. Consequently, $M = 22.50 + 5 = 27.50$. This method solves the problem mentally in under 15 seconds. ### Common Pitfall Students often try to average the difference directly, thinking the average of $M$ and $M-5$ is the overall average. You must account for the weights ($600$ vs $400$); an unweighted average of the two individual wages will lead to an incorrect answer. ### Final Answer **Therefore, the correct answer is Man : ₹ 27.50, Woman : ₹ 22.50.**