A trader has 1000 kg of wheat. He sells a part of it at 8% profit and the rest at 18% profit. On the whole he makes a profit of 14%. How much wheat did he sell at 8% profit?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 400 kg
The overall profit of 14% is a mean of 8% and 18%, so the rule of alligation gives the ratio of the two parts.
Part at 8% \(\propto 18-14=4\)
Part at 18% \(\propto 14-8=6\)
Ratio \(=4:6=2:3\)
Part at 8% \(\displaystyle =\frac{2}{5}\times1000=400\) kg
He sold 400 kg at 8% profit.
Why the other options are incorrect
Option (1) 600 kg — Incorrect. This is the part sold at 18% profit, not at 8%.
Option (2) 640 kg — Incorrect. With 640 kg at 8% the overall profit would be only about 11.6%.
Option (4) 560 kg — Incorrect. With 560 kg at 8% the overall profit would be about 12.4%.