Multiple choice

A dealer mixes \$14 per kg of tea and \$23 per kg of tea and sells that mixture at a price of $22 per kg. What is the proportion of each type of tea that he should mix and sell to earn a profit of 10%?

  1. 2 : 1

  2. 1 : 2

  3. 1 : 4

  4. 4 : 1

  5. 3 : 4
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B Correct answer
Explanation

Let the ratio be x:y. The cost price of the mixture is 22 / 1.1 = 20. Using the alligation rule: (23 - 20) / (20 - 14) = 3 / 6 = 1 / 2.

AI explanation

To earn a 10% profit on a selling price of \$22, the cost price of the mixture must be 22 divided by 1.1, which is \$20. Using the rule of alligation with the two costs of $14 and $23 against the mean price of $20, the ratio of the first tea to the second tea is (23 minus 20) to (20 minus 14). This gives a required proportion of 3 : 6, which simplifies to 1 : 2.

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