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 had calculated that if he sells 100% more woollen trousers than cotton trousers, his overall profit would 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%

Hint:

Overall profit is a cost-weighted average; first find the cost ratio of woollen to cotton trousers from the planned 45% profit, then reapply it with the actual quantity ratio.

Answer 1

The Correct Option is B

Step 1: Assume convenient cost prices and planned quantities.
Overall profit percentage depends on the cost value of each type sold, so let the cost price of one cotton trouser be Rs 100 and one woollen trouser be Rs \(y\) (to be found). Since he planned to sell 100% more woollen trousers than cotton trousers, take a planned sale of 10 cotton and 20 woollen trousers.

Step 2: Use the planned 45% profit to find \(y\).
Total planned cost \(= 10(100) + 20(y) = 1000 + 20y\).
Total planned profit \(= 10(100)(0.30) + 20(y)(0.50) = 300 + 10y\).
\[ \frac{300 + 10y}{1000 + 20y} = 0.45 \]
\[ 300 + 10y = 450 + 9y \]
\[ y = 150 \]
So a woollen trouser costs 1.5 times as much as a cotton trouser.

Step 3: Apply the actual sales ratio.
He actually sold 50% more cotton trousers than woollen trousers, so take 15 cotton and 10 woollen trousers as actual sales (same 3 : 2 ratio). Cost prices stay Rs 100 and Rs 150.

Step 4: Find the actual overall profit.
Total actual cost \(= 15(100) + 10(150) = 1500 + 1500 = 3000\).
Total actual profit \(= 15(100)(0.30) + 10(150)(0.50) = 450 + 750 = 1200\).
\[ \text{Overall profit} = \frac{1200}{3000} = 0.40 = 40\% \]

Final Answer:
The overall profit works out to 40%, so option B is correct. The other values do not satisfy the 45% planned-profit condition used to fix the cost ratio. \[ \boxed{40\%} \]