Multiple choice

In the given questions, two quantities are given, one as ‘Quantity I’ and another as ‘Quantity II’. You have to determine relationship between two quantities and choose the appropriate option: Quantity I: A shopkeeper mixes two varieties of rice, one at the rate of Rs 12/kg and the other at Rs 28/kg in the ratio of a:b and sells the mixture at Rs 30/kg thereby gaining 66.66% on the transaction. But if he mixes them in the ratio of b:a and sells the mixture at the same price of Rs 30/kg, then what would be his gain%? Quantity II: A shopkeeper mixes two varieties of rice, one at the rate of Rs 12/kg and the other at Rs 28/kg in the ratio 2:3. If he sold the mixture at Rs 27/kg, then his profit percentage is:

  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 no relation
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A Correct answer
Explanation

Quantity I: Cost price of mixture = 30/(1 + 2/3) = Rs 18/kg. Using alligation on Rs 12 and Rs 28 with mean Rs 18 gives ratio 2:1 (a:b = 2:1). When ratio reversed to 1:2, new cost = (1*12 + 2*28)/3 = Rs 68/3 ≈ Rs 22.67. Gain% = (30 - 68/3)/(68/3) * 100 = 33.33%. Quantity II: With ratio 2:3, cost = (2*12 + 3*28)/5 = Rs 108/5 = Rs 21.60. Profit% = (27 - 21.60)/21.60 * 100 = 25%. Since 33.33% > 25%, Quantity I > Quantity II is correct.

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