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?Options78 kg67 kg90 kg89 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?Options78 kg67 kg90 kg89 kg
Solution
To solve this problem, we can use the method of allegation, which is a rule of mixtures to find the mean or average value in certain cases in arithmetic.
Step 1: Identify the two types of profits. The trader sells some sugar at 10% profit and the rest at 25% profit.
Step 2: The mean profit is given as 15%.
Step 3: Now, we calculate the differences between the mean profit and the two types of profits. The difference between 25% and 15% is 10%, and the difference between 15% and 10% is 5%.
Step 4: The ratio of the quantities of sugar sold at 25% profit to 10% profit is therefore 5:10, which simplifies to 1:2.
Step 5: This means that for every 1 kg of sugar sold at 25% profit, 2 kg of sugar is sold at 10% profit.
Step 6: The total quantity of sugar is 200 kg. So, we divide this into 3 parts (since 1+2=3). Each part is therefore 200/3 = 66.67 kg.
Step 7: The quantity of sugar sold at 25% profit is 1 part, which is 66.67 kg.
So, the closest option is 67 kg.
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