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: Wine costing \$40 per litre is mixed with wine costing \$50 per litre such that the mixture costs \$44 per litre. Calculate the percentage of wine costing \$40 in the mixture. Quantity II: Vodka costing \$54 per litre is mixed with vodka costing \$60 per litre so as to earn a profit of 15% after selling the mixture for \$64.4 per litre. Calculate the percentage of vodka costing \$54 in the mixture.

  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
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Using alligation, (50-44)/(44-40) = 6/4 = 3/2. Ratio of 40:50 is 3:2. Percentage of 40 = 3/(3+2) = 60%. Quantity II: Selling price = 64.4, profit = 15%. Cost price = 64.4 / 1.15 = 56. Using alligation, (60-56)/(56-54) = 4/2 = 2/1. Ratio of 54:60 is 2:1. Percentage of 54 = 2/(2+1) = 66.67%. 60% < 66.67%.

AI explanation

Using the rule of alligation for Quantity I, the ratio of the \$40 wine to the \$50 wine is (50 - 44) : (44 - 40), which is 6 : 4 or 3 : 2. The percentage of the \$40 wine in the mixture is 3 / (3 + 2) = 60%. For Quantity II, to earn a 15% profit on the selling price of \$64.4, the average cost price of the mixture must be 64.4 / 1.15 = \$56 per litre. Using alligation again, the ratio of the \$54 vodka to the \$60 vodka is (60 - 56) : (56 - 54), which is 4 : 2 or 2 : 1. The percentage of the \$54 vodka in the mixture is 2 / (2 + 1) = 66.67%. Quantity I is less than Quantity II.

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