Question

A man sells an article at a loss of 10%. If he had sold it for Rs. 50 more, he would have gained 5%. What is the cost price?

• A. Rs. 300
• B. Rs. 333.33
• C. Rs. 350
• D. Rs. 400

Hint:

Set up equations based on percentage loss and gain to find cost price.

Answer 1

The Correct Option is B

- Step 1: Let cost price = $C$. Selling price at 10% loss = $C \times 0.9$.
- Step 2: Selling price at 5% gain = $C \times 1.05$.
- Step 3: Given: $C \times 1.05 = C \times 0.9 + 50$.
- Step 4: Solve: $1.05C - 0.9C = 50 \implies 0.15C = 50 \implies C = \frac{50}{0.15} = \frac{500}{1.5} = 333.33$.
- Step 5: Verify: Loss SP = $333.33 \times 0.9 = 300$, Gain SP = $333.33 \times 1.05 = 350$, difference = 50.
- Step 6: Option (2) is Rs. 333.33, correct.