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?Options90 kg89 kg78 kg67 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?Options90 kg89 kg78 kg67 kg
Solution
To solve this problem, we can use the method of allegation, which is a rule of mixture to find the mean or average value in a mixture when the quantities of all ingredients, mixed together, are given.
Step 1: Identify the profits of each part and the mean profit.
The profit on the first part of the sugar is 10%, the profit on the second part is 25%, and the overall profit is 15%.
Step 2: Calculate the differences between the mean profit and the profits of each part.
The difference between the mean profit and the profit on the first part is 15% - 10% = 5%. The difference between the mean profit and the profit on the second part is 25% - 15% = 10%.
Step 3: Find the ratio of the quantities of each part.
The ratio of the quantities of the first part to the second part is the inverse of the ratio of their differences, which is 10 : 5 = 2 : 1.
Step 4: Apply the ratio to the total quantity.
The total quantity of sugar is 200 kg. According to the ratio, the quantity of sugar sold at 25% profit is 200 kg * (1 / (2 + 1)) = 66.67 kg.
So, the closest answer is 67 kg.
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