Multiple choice

McGrath earned a profit of Rs. 300 by selling 100 kg of a mixture of A and B types of rice at a total price of Rs. 1100. What was the proportion of A and B types of rice in the mixture, if the cost prices of A and B were Rs. 10 per kg and Rs. 5 per kg, respectively?

  1. 3 : 2

  2. 13 : 18

  3. 2 : 3

  4. 8 : 11
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A Correct answer
Explanation

Total quantity = 100 kg, Total SP = 1100, Profit = 300, so Total CP = 800. Let A = x, B = 100-x. 10x + 5(100-x) = 800. 10x + 500 - 5x = 800. 5x = 300, x = 60. A = 60, B = 40. Ratio = 60:40 = 3:2.

AI explanation

The total cost price of the mixture is 1100 minus 300, which equals Rs. 800 for 100 kg, giving a cost price of Rs. 8 per kg. Using the rule of alligation with the costs of rice A (Rs. 10) and rice B (Rs. 5), the ratio of their quantities is calculated as (8 - 5) : (10 - 8). This simplifies to 3 : 2, giving the proportion of A and B types of rice in the mixture.

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