A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is

To solve this problem, we can use the concept of weighted averages. Here's how:

1. Let's denote the amount of sugar sold at 8% profit as 'x' kg and the amount sold at 18% profit as '1000 - x' kg (since the total amount of sugar is 1000 kg).

2. According to the problem, the merchant gains 14% on the whole. This means that the weighted average profit of the two parts is 14%. We can express this as follows:

   (8% * x + 18% * (1000 - x)) / 1000 = 14%

3. Simplifying this equation gives us:

   0.08x + 180 - 0.18x = 140

4. Solving for 'x' gives us:

   0.1x = 40

   x = 400

5. Therefore, the amount of sugar sold at 18% profit is 1000 - x = 1000 - 400 = 600 kg.

So, the merchant sold 600 kg of sugar at 18% profit.

To solve this problem, we can use the concept of weighted averages. Here's how:

1. Let's denote the amount of sugar sold at 8% profit as 'x' kg and the amount sold at 18% profit as '(1000 - x)' kg.

2. The total profit is 14% of the total weight, which is 1000 kg. So, the total profit is 14/100 * 1000 = 140 kg.

3. The profit from the sugar sold at 8% is 8/100 * x = 0.08x kg.

4. The profit from the sugar sold at 18% is 18/100 * (1000 - x) = 180 - 0.18x kg.

5. Since the total profit is the sum of the profits from the sugar sold at 8% and 18%, we can set up the following equation:

   0.08x + 180 - 0.18x = 140

6. Simplifying the equation gives:

   -0.1x = -40

7. Solving for 'x' gives:

   x = 400

So, the merchant sold 400 kg of sugar at 8% profit and the rest, which is 1000 - 400 = 600 kg, at 18% profit.