A trader has 1,200 kg of rice. He sells a part of it at 10% profit and the rest at 25% profit. On the whole he makes a profit of 20%. How much rice did he sell at 10% profit?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 400 kg
By alligation, the two quantities are in the ratio of the distances of the other profit from the overall profit.
At 10% : at 25% \(=(25-20):(20-10)=5:10\)
Quantity at 10% \(\displaystyle =\frac{5}{15}\times1200=400\) kg
He sold 400 kg at 10% profit.
Why the other options are incorrect
Option (1) 600 kg — Incorrect. Selling 600 kg at 10% and the rest at 25% gives an overall profit of 17.5%, not 20%.
Option (2) 300 kg — Incorrect. Selling 300 kg at 10% and the rest at 25% gives an overall profit of 21.25%, not 20%.
Option (3) 800 kg — Incorrect. Selling 800 kg at 10% and the rest at 25% gives an overall profit of 15%, not 20%.