Multiple choice

Directions: In these questions, two quantities numbered I and II are given. You have to solve both the quantities and give answer An article was sold at a profit of Rs 144 such that a discount of 25% was allowed while selling. The article was marked up at Rs 432 more than its cost price. Quantity I: The selling price of the article Quantity II: If the article was marked up at Rs 140 more than its cost price, what would have been the marked price of the article?

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or a relation can't be established
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A Correct answer
Explanation

Let CP = x. Then MP = x + 432. SP = MP * 0.75 = 0.75(x + 432). Profit = SP - CP = 144. So 0.75x + 324 - x = 144, which means 0.25x = 180, so x = 720. Quantity I (SP) = 720 + 144 = 864. Quantity II: If MP = x + 140 = 720 + 140 = 860. Since 864 > 860, Quantity I > Quantity II.

AI explanation

Let the cost price be CP and the marked price be MP. From the given information, Profit = 0.75 * MP - CP = 144, and MP = CP + 432. Substituting the second equation into the first gives 0.75 * (CP + 432) - CP = 144, which simplifies to 0.25CP = 180, meaning CP is 720 and MP is 1152. Quantity I is the selling price, which is 0.75 * 1152 = 864. For Quantity II, the marked price when marked up by Rs. 140 is 720 + 140 = 860. Therefore, Quantity I is greater than Quantity II.

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