Multiple choice

How many kilograms of sugar of Rs.5.4 per kg should be mixed with 10 kg of sugar of Rs.4.5 per kg, such that there may be gain of 20% by selling the mixture at Rs.5.94 per kg.

  1. 10 kg

  2. 12 kg

  3. 15 kg

  4. 8 kg

  5. 9 kg
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A Correct answer
Explanation

Let x be the kg of sugar at 5.4. Total cost = 5.4x + 4.5*10. Selling price for 20% gain = 1.2 * (5.4x + 45) / (x + 10) = 5.94. Solving this: 6.48x + 54 = 5.94x + 59.4, which gives 0.54x = 5.4, so x = 10 kg.

AI explanation

The selling price of the mixture is Rs 5.94 per kg, and since this includes a 20% gain, the cost price of the mixture is 5.94 divided by 1.2, which equals Rs 4.95 per kg. Using the Rule of Alligation, the difference between the Rs 4.95 mean price and the Rs 4.5 sugar is 0.45, while the difference with the Rs 5.4 sugar is 0.45. This gives an equal mixing ratio of 1:1, meaning exactly 10 kg of the Rs 5.4 sugar should be mixed with the 10 kg of Rs 4.5 sugar.

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