Multiple choice

Shweta purchased a variety of rice at Rs. 65 per kg and mixed it with 5 kg of another variety of rice that she had purchased at Rs. 58 per kg. If she gains 10% on selling the mixture at Rs. 66 per kg, then what was the quantity of rice that she had purchased at Rs. 65 per kg?

  1. 1 kg

  2. 2 kg

  3. 3 kg

  4. 5 kg

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the quantity of rice at 65 Rs/kg. Total cost = 65x + 5*58. Selling price = 66(x+5). Profit is 10%, so 1.1 * (65x + 290) = 66(x+5). Solving for x gives 71.5x + 319 = 66x + 330, so 5.5x = 11, x = 2.

AI explanation

The selling price of Rs. 66 per kg includes a 10 percent profit, so the cost price of the mixture is 66 divided by 1.1, which equals Rs. 60 per kg. Using the rule of alligation with the Rs. 58 per kg rice and the Rs. 65 per kg rice, the ratio of their quantities is (65 minus 60) to (60 minus 58), which is 5 to 2. Since the 2 parts correspond to the 5 kg of the cheaper variety, 5 parts correspond to a quantity of 2 kg for the Rs. 65 per kg rice. However, if the profit percentage was intended to be 10 percent, the resulting quantity would be 12.5 kg.

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