Multiple choice

Passage

Directions: Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You are to use the given data and your knowledge of Mathematics to choose among the given options.

Quantity I: Mr. X bought two mobile phones and paid \$2550 for each. He sold one mobile phone at a profit of 24% to one customer and the second phone to another customer at a profit of 18% more than the percentage profit he made on selling the first phone. Difference between the selling prices of both the mobile phones Quantity II: Mr. Y bought a mobile phone and marked up 10% above its cost price, while on selling the mobile phone, he gave a discount of 5% to his customer. Cost price of the mobile phone if he earned \$18 as profit

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I = Quantity II or no relation can be established.

  5. Quantity I ≤ Quantity II
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A Correct answer
Explanation

Quantity I: The first phone is sold at 24% profit, so SP1 = 2550 * 1.24 = 3162. The second is sold at 24% + 18% = 42% profit, so SP2 = 2550 * 1.42 = 3621. The difference is 3621 - 3162 = 459. Quantity II: Let CP be x. Markup is 10%, so MP = 1.1x. Discount is 5%, so SP = 1.1x * 0.95 = 1.045x. Profit = 0.045x = 18, so x = 18 / 0.045 = 400. Since 459 > 400, Quantity I > Quantity II.

AI explanation

For Quantity I, the profit on the second phone is 24% + 18% = 42%, so the difference in selling prices is (0.42 - 0.24) * 2550 = 459. For Quantity II, the profit equals 10% markup minus 5% discount, yielding a 4.5% overall profit. If 4.5% of the cost price is \$18, the cost price is 18 / 0.045 = \$400. Since 459 is greater than 400, Quantity I > Quantity II.

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