Question

A firm of readymade garments make both men's and women's shirt. Its profit average is $6$% of sales. Its profits in men's shirt average $8$% of sales and women's shirts comprise $60$% of output. The average profit per sales rupee in women's shirts is :

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

Answer 1

The correct option is A $0.0466$

Here $\overline{x}=6,\overline{x_1}=8,n_1=40,n_2=60$.
Assuming that the total output is $100,$ we are required to find out $\overline{x_2}$, we know that
$\overline{x}=\frac{n_1\overline{x_1}+n_2\overline{x_2}}{n_1+n_2}=\frac{40\times 8+60\overline{x_2}}{40+60}$
$\Rightarrow 6=\frac{320+60\overline{x_2}}{100}\Rightarrow \overline{x_2}=\frac{600-320}{60}=\frac{280}{60}=4.66$
Thus, the average profit in womens shirt is $4.66$% of sales or $Rs0.0466$ per sale rupee.