A trader has 200 kg of sugar, out of which he sells some with 10% profit and the rest with 25% profit. He gains 15% on the whole. Find the quantity of sugar sold at 25% profit?Options89 kg78 kg67 kg90 kg
Question
A trader has 200 kg of sugar, out of which he sells some with 10% profit and the rest with 25% profit. He gains 15% on the whole. Find the quantity of sugar sold at 25% profit?Options89 kg78 kg67 kg90 kg
Solution
To solve this problem, we can use the concept of weighted averages.
Let's denote:
- X as the amount of sugar sold at 10% profit
- Y as the amount of sugar sold at 25% profit
We know that X + Y = 200 kg (the total amount of sugar)
The overall profit is 15%, so we can set up the following equation:
(X * 10% + Y * 25%) / 200 = 15%
Solving this equation for Y gives us:
Y = (15% * 200 - X * 10%) / 25%
We also know that X + Y = 200, so we can substitute X = 200 - Y into the previous equation:
Y = (15% * 200 - (200 - Y) * 10%) / 25%
Solving this equation for Y gives us:
Y = 80 kg
So, the trader sold 80 kg of sugar at 25% profit. However, this option is not available in the given options. There might be a mistake in the problem or the options provided.
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