Question

A firm readymade garments makes both men’s and women’s shirts. Its average profit is 6% of sales. Its profits in men’s shirts 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.0.0666
c.0.0166
d.None of these

Answer 1

Hint: Assume the total cost of sales be Rs. x and average profit for women’s shirts be y %. The price of sales of men’s shirts is 40% of x and the price of sales of women’s shirts is 60% of x. Now, calculate the total profit of men’s shirts and calculate the total profit of women’s shirts. Total profit is the summation of total profit of men’s shirts and total profit of women’s shirts. Now, solve further and get the value of y.

Complete step-by-step answer:
Let the total cost of sales be of Rs. x and average profit for women’s shirts be y %.
According to the question, it is given that,
Percentage of share of women’s shirt in total output = 60%,
Percentage of share of men’s shirt in total output = (100 - 60) % = 40%,
Percentage of average profit of men’s shirts = 8%,
Percentage of the total average profit = 6%.
The price of sales of men’s shirts = 40% of x.
Also, we have the percentage of average profit of men’s shirts = 8%,
Now, the total profit of men’s shirt = 8% of 40% of x = \[\dfrac{8}{100}\times \dfrac{40}{100}x\] ………………(1)
The price of sales of women’s shirts = 60% of x.
Also, we have the percentage of average profit of women’s shirts = y%,
Now, the total profit of women’s shirt = y% of 60% of x = \[\dfrac{y}{100}\times \dfrac{60}{100}x\] ………………(2)
Total profit = 6% of x = \[\dfrac{6}{100}x\] ……………………..(3)
Total profit = The total profit of men’s shirt + The total profit of men’s shirt.
Now, from equation (1), equation (2), and equation (3), we get
\[\begin{align}
  & \dfrac{6}{100}x=\dfrac{8}{100}\times \dfrac{40}{100}x+\dfrac{y}{100}\times \dfrac{60}{100}x \\
 & \Rightarrow 600x=320x+60xy \\
 & \Rightarrow 600-320=60y \\
 & \Rightarrow 280=60y \\
 & \Rightarrow \dfrac{280}{60}=y \\
 & \Rightarrow 4.66=y \\
\end{align}\]
The average profit per sales rupee in women’s shirts = \[\dfrac{4.66}{100}=0.0466\] .
Hence, the correct option is A.

Note: In this type of question, one can make a mistake in percentage. It means one may forget to divide the percentage term by 100 during calculations. Like, 8% of 40% of x should be written as \[\dfrac{8}{100}\times \dfrac{40}{100}x\] not as \[8\times 40\times x\] , \[\dfrac{8}{100}\times 40x\] , or \[8\times \dfrac{40}{100}x\] . So, it should be remembered that we divide by 100 in percentage terms for removing the percentage sign.