A firm of readymade garments makes both men's and women's shirts. Its average profit is 6% of the sales. Its profit in men's shirts average 8% of the sales and women's shirts comprise 60% of the output. The average profit per sales rupee in women's shirts is (M.A.T., 2006)

### Concept & Weighted Average The overall average profit percentage is the weighted average of the profit percentages of the individual categories (men's and women's shirts) based on their sales volume. $$ \text{Total Profit} = \text{Profit}_{\text{Men}} + \text{Profit}_{\text{Women}} $$ ### Step-by-Step Solution * Let the total sales volume (in rupees) be $100x$. * The overall average profit is $6\%$ of sales, so Total Profit = $6x$. * Women's shirts comprise $60\%$ of the output. Assuming sales value is proportional to output, sales of women's shirts = $60x$, and sales of men's shirts = $40x$. * The profit on men's shirts is $8\%$ of their sales. Profit on men's shirts = $8\%$ of $40x = 3.2x$. * Let the profit on women's shirts be $P_w$. * Total Profit = Profit on men's shirts + Profit on women's shirts * $6x = 3.2x + P_w$ * $P_w = 6x - 3.2x = 2.8x$. * The average profit per sales rupee in women's shirts = $\frac{\text{Profit on women's shirts}}{\text{Sales of women's shirts}}$. * $\frac{2.8x}{60x} = \frac{2.8}{60} = \frac{28}{600} = \frac{7}{150} \approx 0.0466$. ### Exam Strategy & Shortcut Use the rule of alligation. Let $w$ be the profit percentage of women's shirts. Ratio of men's to women's sales is $40:60 = 2:3$. Using alligation on profit percentages: $\frac{w - 6}{6 - 8} = \frac{2}{3} \implies 3w - 18 = -4 \implies 3w = 14 \implies w = 4.66\%$. As a decimal per rupee, $4.66\%$ is $0.0466$. ### Common Pitfall Students often forget to convert the final percentage ($4.66\%$) into a "per rupee" decimal value, confusing $4.66$ with $0.0466$. ### Final Answer Therefore, the correct answer is **0.0466**.