Multiple choice

In what ratio must two kinds of tea worth Rs 18 and Rs 28 per kg be mixed so that by selling the mixture at Rs 32 per kg, there may be a gain of 20%.

  1. 2 : 13

  2. 1 : 13

  3. 3 : 14

  4. 2 : 3
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A Correct answer
Explanation

Selling price = 32, gain = 20%. Cost price = 32 / 1.2 = 320 / 12 = 80 / 3 = 26.67. Using alligation between 18 and 28 with mean 80/3: (28 - 80/3) : (80/3 - 18) = (4/3) : (26/3) = 4 : 26 = 2 : 13.

AI explanation

First find the cost price of the mixture by dividing the selling price of Rs 32 by 1.20, which gives a cost price of Rs 80/3 per kg. Using the rule of alligation with the two tea prices of Rs 18 and Rs 28, the ratio is calculated as (80/3 minus 28) to (18 minus 80/3). This evaluates to (-4/3) for the first quantity and (-26/3) for the second, indicating the cost price is outside the range of the two initial prices. The absolute ratio of the differences is 4/3 to 26/3, which simplifies by multiplying by 3 to 4 to 26, resulting in a ratio of 2:13. The required mixing ratio is 2:13.

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