Multiple choice

Directions: In the question, two quantities are given, one as 'Quantity 1' and the other as 'Quantity 2'. You have to determine the relationship between the two quantities and choose the appropriate option. The labelled price of a laptop bag is Rs. 1500 and two successive discounts, each of x% on the marked price, are equal to a single discount of Rs. 587.40. Quantity 1: Value of the selling price of the laptop bag, if a single discount of x% is given on the marked price Quantity 2: Value of 47/42 of the selling price of the laptop bag, if a single discount of (x + 8)% is given on the marked price

  1. Quantity 1 < Quantity 2

  2. Quantity 1 > Quantity 2

  3. Quantity 2 ≥ Quantity 1

  4. Quantity 1 ≥ Quantity 2

  5. Quantity 1 = Quantity 2 or Relation cannot be established
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A Correct answer
Explanation

Two successive discounts of x% on 1500 = 587.40. 1500 * (1 - x/100)^2 = 1500 - 587.40 = 912.60. (1 - x/100)^2 = 0.6084. 1 - x/100 = 0.78, so x = 22. Quantity 1: SP with 22% discount = 1500 * 0.78 = 1170. Quantity 2: SP with 30% discount = 1500 * 0.7 = 1050. 47/42 * 1050 = 1175. Since 1170 < 1175, Q1 < Q2.

AI explanation

Using the successive discount formula, the final selling price after two discounts of x percent is 1500 times (1 minus x divided by 100) squared, which equals 1500 minus 587.40. Solving (1 minus x divided by 100) squared equals 0.6084 gives x equals 22, so a single discount of 22 percent results in Quantity 1 being 1500 times 0.78, which is 1170. For Quantity 2, the selling price with a 30 percent discount is 1500 times 0.70, which equals 1050, and 47 divided by 42 of this value is 1175. Therefore, Quantity 1 is less than Quantity 2.

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