A trader had 12 quintals of wheat. He sold a part of it at 13% profit and the rest at 23% profit, so that he made a total profit of 17%. How much wheat did he sell at 23% profit?

We can apply the method of alligation to solve this problem.
Profit percent on Part 1 = 13%
Profit percent on Part 2 = 23%
Overall mean profit percent = 17%

Using alligation:

Part 1 (13%) Part 2 (23%)
\ /
\ /
Mean (17%)
/ \
/ \
(23 - 17) (17 - 13)
= 6 = 4
The ratio of weights of Part 1 to Part 2 is 6:4, which simplifies to 3:2.

Total weight of wheat = 12 quintals = 12×100kg=1200kg.

The quantity of wheat sold at 23% profit (Part 2):

Weight=
3+2
2
​
×1200kg
Weight=
5
2
​
×1200=2×240=480kg