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In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: A shopkeeper earned a profit of 11.5% on a product after selling it at a discount of 10%. At what percentage above the cost price did he marked the price of the product? Quantity B: A shopkeeper marked a product at 45% above its cost price. After selling it at a certain discount, he earns a profit of 15%. Find the discount percentage.

In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: A shopkeeper earned a profit of 11.5% on a product after selling it at a discount of 10%. At what percentage above the cost price did he marked the price of the product? Quantity B: A shopkeeper marked a product at 45% above its cost price. After selling it at a certain discount, he earns a profit of 15%. Find the discount percentage. Correct Answer Quantity A > Quantity B

Solving for Quantity A:

Let the cost price be Rs. ‘x’

Profit = 11.5% of x = 0.115x

Selling price = Cost price + profit = x + 0.115x = 1.115x

Now, Marked price - Discount = Selling price

⇒ MP - 10% of MP = 1.115x

⇒ 0.9MP = 1.115x

⇒ MP = 1.115x/0.9 = 1.24x

⇒ MP = (100 + 24)% of x

The marked price of the product is 24% above its cost price

⇒ Quantity A = 24%

Solving for Quantity B:

Let the cost price be Rs. ‘x’ and the discount be ‘d’%

Profit = 15% of x = 0.15x

Selling price = Cost price + profit = x + 0.15x = 1.15x

Marked price = (100 + 45)% of x = 1.45x

Now, Marked price - Discount = Selling price

⇒ 1.45x - d% of 1.45x = 1.15x

⇒ (d/100) × 1.45x = 1.45x - 1.15x

⇒ d = (0.3x/1.45x) × 100 = 20.7%

⇒ Quantity B = 20.7%

∴ Quantity A > Quantity B

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