A trader has 1000 kg of sugar. He sells a part of it at 8% profit and the rest at 18% profit. His profit on the whole is 14%. How many kg of sugar did he sell at 18% profit?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 600 kg
The overall profit of 14% is the mean of the two rates, so the rule of alligation gives the ratio of the two quantities.
\(\text{Quantity at } 8\% : \text{Quantity at } 18\% = (18 - 14) : (14 - 8)\)
\(= 4 : 6 = 2 : 3\)
\(\displaystyle \text{Quantity at } 18\% = \frac{3}{5} \times 1000 = 600 \text{ kg}\)
So 600 kg was sold at 18% profit. Check: \(8\% \text{ of } 400 + 18\% \text{ of } 600 = 32 + 108 = 140\), which is 14% of 1000.