A trader had 6 quintals of wheat. He sold a part of it at 7% profit and the rest at 17% profit, so that he made a total profit of 11%. How much wheat did he sell at 17% profit?

Given:
Total quantity of wheat = 6 quintals=6×100 kg=600 kg
Profit on first part = 7%
Profit on second part = 17%
Overall profit = 11%

Using the method of allegation:

Profit on Part 1
7%
(17−11)
=6
​

↘↙
11%
↙↘
​

Profit on Part 2
17%
(11−7)
=4
​

Ratio of the quantities sold at 7% profit to 17% profit is:

Ratio=6:4=3:2
Quantity of wheat sold at 17% profit:

=
3+2
2
​
×600 kg
=
5
2
​
×600 kg=240 kg