Question

A salesman sells two kinds of trousers: cotton and woollen. A pair of cotton trousers is sold at 30$\%$ profit and a pair of woollen trousers is sold at 50$\%$ profit. The salesman has calculated that if he sells 100$\%$ more woollen trousers than cotton trousers, his overall profit will be 45$\%$ . However, he ends up selling 50$\%$ more cotton trousers than woollen trousers. What will be his overall profit?

• A. 37.5
• B. 40
• C. 41
• D. 42.33
• E. None of these

Answer 1

The correct option is B

40

Let the cost price of a cotton trouser and a woollen trouser be ‘x’ and ‘y’ respectively.
If number of woollen trousers sold is 100$\%$ more than cotton trousers, then
$\Rightarrow$1.3x + 1.5 $\times$ 2 $\times$ y = 1.45 (x + 2y)
0.15x = 0.1y
3x = 2y
$\therefore$ y = $\frac{3}{2}$ x

Now, if the number of cotton trousers sold is 50$\%$ more than woollen trousers, then
$S.P.=1.3x+\frac{1.5\times 2y}{3}=1.3x+y=1.3x+1.5x=2.8xC.P.=x+\frac{2}{3}y=x+x=2x$

Required profit = $\frac{2.8x-2x}{2x}\times 100=\frac{0.8x}{2x}\times 100=\frac{8}{20}\times 100=40\%$