A trader has 100 Kg of wheat, part of which he sells at 5% profit and the rest at 20% profit. He gains 15% on the whole. Find how much is sold at 5% profit?

This is a mixture problem using allegation. The overall profit (15%) is exactly in the middle of 5% and 20%, so equal quantities must be sold at each profit rate. But the claimed answer is 33.3 kg at 5% profit. Let me verify: if x kg at 5%, then (100-x) kg at 20%. Overall profit = [5x + 20(100-x)]/100 = [2000 - 15x]/100 = 15. Solving: 2000 - 15x = 1500, so 15x = 500, x = 33.33 kg. The answer 33.3 kg is correct.