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A merchant has 2000 kg of sugar, part of which he sells at 16% profit and the rest at 36% profit. He gains 28% on the whole. The quantity sold at 36% profit is: Options : 800 1000 1200 600

Question

A merchant has 2000 kg of sugar, part of which he sells at 16% profit and the rest at 36% profit. He gains 28% on the whole. The quantity sold at 36% profit is: Options : 800 1000 1200 600

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Solution

Let's solve this step by step:

  1. Let's assume that the quantity of sugar the merchant sells at 36% profit is x kg. Therefore, the quantity of sugar he sells at 16% profit is (2000 - x) kg.

  2. The overall profit made by the merchant is 28%. So, the total profit from 2000 kg of sugar is 28% of 2000 kg.

  3. The profit from the sugar sold at 16% profit is 16% of (2000 - x) kg and the profit from the sugar sold at 36% profit is 36% of x kg.

  4. According to the problem, the sum of the profit from the sugar sold at 16% and the profit from the sugar sold at 36% should be equal to the total profit. So, we can set up the following equation:

    16/100 * (2000 - x) + 36/100 * x = 28/100 * 2000

  5. Solving this equation will give us the value of x, which is the quantity of sugar sold at 36% profit.

  6. Simplifying the equation gives:

    320 - 0.16x + 0.36x = 560

  7. Combining like terms gives:

    0.2x = 240

  8. Solving for x gives:

    x = 240 / 0.2 = 1200

So, the merchant sold 1200 kg of sugar at a 36% profit. Therefore, the correct answer is 1200.

This problem has been solved

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