Multiple choice

Manish purchases a particular variety of rice at Rs. 21 per kg and mixes it with 25 kg of another variety of rice purchased at Rs. 12 per kg. If he gains 25% on selling the mixture at Rs. 20 per kg, find the quantity of rice that he purchased at Rs. 21 per kg.

  1. 15 kg

  2. 18 kg

  3. 20 kg

  4. 23 kg

  5. 25 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the quantity of rice at Rs. 21/kg. The total cost is 21x + (25 * 12). The total revenue from selling (x + 25) kg at Rs. 20/kg with a 25 percent gain is (Total Cost * 1.25) = 20(x + 25). Solving 1.25 * (21x + 300) = 20x + 500 leads to 26.25x + 375 = 20x + 500, so 6.25x = 125, giving x = 20 kg.

AI explanation

The selling price of 20 rupees per kg represents a 25 percent gain, so the cost price of the mixture is 20 divided by 1.25, which equals 16 rupees per kg. Using the method of alligation with the prices of 21 rupees and 12 rupees against the mean of 16 rupees, subtract diagonally to get 4 parts of the 12 rupee rice and 5 parts of the 21 rupee rice. Since the 12 rupee rice quantity is 25 kg, the proportion gives 5 divided by 4 times 25, which equals 20 kg of the 21 rupee rice.

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