Question

A firm of readymade garments makes both men's and women's shirts. Its average profit is $6\%$ of the sales. Average profit in men's shirts is $8\%$ of the sales and women's shirts comprise $60\%$ of the output. The average profit per sale rupee in women's shirts is:

• A. $0.0466$
• B. $0.0666$
• C. $0.0166$
• D. None of these

Hint:

When an overall percentage is a mix of two groups, use a weighted average with \emph{sales share} as weights. Here: $0.06=0.4(0.08)+0.6(x)$.

Answer 1

The Correct Option is A

Step 1 (Let the women's profit rate be $x$).
Let the sales proportions be: men $=40\%$ (since women are $60\%$), women $=60\%$.
Given: overall average profit rate $=6\%=0.06$, men's rate $=8\%=0.08$, women's rate $=x$. Step 2 (Weighted-average equation).
Overall rate $=$ (men's share)$\times$(men's rate)$+$(women's share)$\times$(women's rate): \[ 0.06=0.40\cdot 0.08+0.60\cdot x \Rightarrow 0.06=0.032+0.60x \Rightarrow 0.60x=0.028 \Rightarrow x=\frac{0.028}{0.60}=0.046\overline{6}. \] Step 3 (Answer).
Women's average profit per sale rupee $=\boxed{0.0466\text{ (approximately)} }$.