Multiple choice

Following questions have two quantities as Quantity I and Quantity II. You have to determine the relationship between them and give answer as, Quantity I: A man buys some quantity of rice for Rs. 5800. He sells one-fourth of the rice at a profit of 20 %. At what percentage gain should he sell the remaining three-fourth rice so as to make an overall profit of 12.5 % on the whole transaction? Quantity II: 40 % of the first number is subtracted from the second number, then the answer will be 16 more than the first number. The first number is 80 less than the second number. The first number is what percentage less than the second number?

  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 Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: 1/4 at 20% profit, 3/4 at x% profit, total 12.5%. (1/4*20) + (3/4*x) = 12.5 => 5 + 0.75x = 12.5 => 0.75x = 7.5 => x = 10%. Quantity II: Let numbers be x and y. y - 0.4x = x + 16 => y = 1.4x + 16. Also x = y - 80 => y = x + 80. Equating: 1.4x + 16 = x + 80 => 0.4x = 64 => x = 160. Then y = 240. Percentage less = (240-160)/240 = 80/240 = 33.33%. Since 10% < 33.33%, Quantity I < Quantity II.

AI explanation

For Quantity I, assume the total cost of the rice is Rs. 400, so the one-fourth portion costs Rs. 100 and the three-fourth portion costs Rs. 300. The target overall profit of 12.5% requires a total selling price of Rs. 450. The first portion is sold at a 20% profit for Rs. 120, requiring the remaining portion to be sold for Rs. 330 to reach the target total. The required profit percentage on the remaining portion is ((330 - 300) divided by 300) multiplied by 100, which equals 10%. For Quantity II, let the first number be X and the second number be Y. The equations are Y - 0.40X = X + 16 and Y - X = 80. Solving these equations shows X = 160 and Y = 240, making the first number ((240 - 160) divided by 240) multiplied by 100, which is 33.33% less than the second number. Comparing the two values reveals that Quantity I < Quantity II.

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