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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 both quantities and choose the correct option. Quantity A: A shopkeeper marked the price of a product 25% above its cost price and sold it at a discount of 30%, thereby earning a loss of Rs. 360. At what discount percentage will he earn a profit of Rs. 360? Quantity B: A shopkeeper earns a profit of 10% by marking his goods at 25% above the cost price and allowing a standard discount on the marked price. Find the rate of discount.

In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: A shopkeeper marked the price of a product 25% above its cost price and sold it at a discount of 30%, thereby earning a loss of Rs. 360. At what discount percentage will he earn a profit of Rs. 360? Quantity B: A shopkeeper earns a profit of 10% by marking his goods at 25% above the cost price and allowing a standard discount on the marked price. Find the rate of discount. Correct Answer Quantity A < Quantity B

Quantity A: 

 

Let the cost price of the product be Rs. x

Marked price of product = x + 25% of x = Rs. 1.25x

At a discount of 30%, loss = Rs. 360

Formula∶ Selling price = Cost price – loss

⇒ Selling price of product = Rs. (x – 360)

Formula∶ Marked price – Discount = Selling price

⇒ 1.25x – 30% of 1.25x = (x – 360)

⇒ 1.25x – 0.375x = x – 360

⇒ x – 0.875x = 360

⇒ x = 360/0.125 = Rs. 2880

⇒ Marked price = 1.25 × 2880 = Rs. 3600

Now, to earn a profit of Rs. 360,

Selling price = Cost price + profit = 2880 + 360 = Rs. 3240

⇒ Discount price = 3600 – 3240 = Rs. 360

∴ Required discount percentage = (360/3600) × 100 = 10%

Quantity B:

Let the cost price of goods be x.

Profit percentage = 10%

Selling price of goods = x + {(10/100) × x} = (110/100)x

Mark up percentage above cost price = 25%

Marked price = x + {(25/100) × x} = (125/100)x

Discount = Marked price – Selling price = (125/100)x – (110/100)x = (15/100)x

Discount percentage = (Discount/Marked price) × 100

= {(15/100)x}/{(125/100)x} × 100 = (15/125) × 100

∴ x = 12%

∴ Quantity A < Quantity B

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