Question

A bought an article at a certain price and sold it at 10% profit. B bought the same article at a price 10% lesser than A and sold it at ₹18 lesser than A. B's gain percentage in this deal is 20%. At what price B bought the article?

• A. ₹900
• B. ₹810
• C. ₹880
• D. ₹920

Hint:

When dealing with profit percentages and cost prices, break the problem into smaller parts, starting with the known profit percentages and solve step by step.

Answer 1

The Correct Option is B

Step 1: Let the cost price of A be \( x \).
A sells the article at a 10% profit, so the selling price of A is: \[ \text{Selling Price of A} = x + 10% \times x = 1.1x. \]

Step 2: B's Buying and Selling Prices.
B buys the article at 10% lesser than A, so B's cost price is: \[ \text{Cost Price of B} = x - 10% \times x = 0.9x. \] B sells it at ₹18 lesser than A, so B's selling price is: \[ \text{Selling Price of B} = 1.1x - 18. \] B's gain percentage is 20%, so: \[ \frac{\text{Selling Price of B} - \text{Cost Price of B}}{\text{Cost Price of B}} \times 100 = 20. \] Substitute the values: \[ \frac{(1.1x - 18) - 0.9x}{0.9x} \times 100 = 20. \] Simplify the equation: \[ \frac{0.2x - 18}{0.9x} \times 100 = 20 \implies 0.2x - 18 = 1.8x \implies 18 = 1.6x \implies x = \frac{18}{1.6} = 11.25. \] Thus, the cost price of A is ₹11.25.

Final Answer: \[ \boxed{810} \]