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Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relationships between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. The options represent the relations among the three quantities. A. < B. > C. ≤ D. ≥ E. = Quantity 1: A shopkeeper earns a profit of 24% if he sells a product for Rs.186. What will be his profit percentage, if he sells the product for Rs.180? Quantity 2: A shopkeeper marks the price of a product 50% above its cost price and sells it at a discount of 20%. What is his profit percentage? Quantity 3: Mahesh sold a laptop to Shyam making a profit of 10%. Shyam sold it to Keshav making a profit of 12%. Keshav sold the laptop to Shital at a profit of 15%. By how much percentage the price of the laptop is increased?

Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relationships between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. The options represent the relations among the three quantities. A. < B. > C. ≤ D. ≥ E. = Quantity 1: A shopkeeper earns a profit of 24% if he sells a product for Rs.186. What will be his profit percentage, if he sells the product for Rs.180? Quantity 2: A shopkeeper marks the price of a product 50% above its cost price and sells it at a discount of 20%. What is his profit percentage? Quantity 3: Mahesh sold a laptop to Shyam making a profit of 10%. Shyam sold it to Keshav making a profit of 12%. Keshav sold the laptop to Shital at a profit of 15%. By how much percentage the price of the laptop is increased? Correct Answer E A

Solving for Quantity A:

Let the cost price of the product be Rs. ‘x’

∵ Cost price + Profit = Selling price

⇒ x + 24% of x = 186

⇒ 1.24x = 186

⇒ x = 186/1.24 = Rs. 150

When the selling price = Rs. 180,

⇒ Profit earned = 180 – 150 = Rs. 30

⇒ Profit percentage = 30/150 × 100 = 20%

⇒ Quantity A = 20%

Solving for Quantity B:

Let the cost price of the product be Rs. ‘x’

⇒ Marked price = x + 50% of x = 1.5x

⇒ Discount = 1.5x – 20% of 1.5x = 1.5x – 0.3x = 1.2x

⇒ Selling price = Marked price – Discount = 1.5x – 0.3x = 1.2x

⇒ Profit earned = 1.2x – x = 0.2x

⇒ Profit percentage = 0.2x/x × 100 = 20%

⇒ Quantity B = 20%

Solving for Quantity C:

Let the original price of the laptop be Rs. ‘x’

Price for Shyam = (100 + 10) % of x = 1.10x

Price for Keshav = (100 + 12) % of 1.10x = 1.12 × 1.10x = 1.232x

Price for Shital = (100 + 15) % of 1.232x = 1.15 × 1.232x = 1.4168x

Hence,

Increase in price of laptop = 1.4168x – x = 0.4168x

∴ Percentage increase = (0.4168x/x) × 100 = 41.68%

∴ Quantity A = Quantity B < Quantity C

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