Let C1 be the cost price of the first article and C2 be the cost price of the second article.
Let the first article be sold at a profit of 22%, while the second one be sold at a loss of 8%.
We know, C1+C2=600.
The first article was sold at a profit of 22%.
∴, the selling price of the first article =C1+(22100)C1=1.22C1
The second article was sold at a loss of 8%.
∴, the selling price of the second article =C2−(8100)C2=0.92C2.
The total selling price of the first and second article =1.22C1+0.92C2.
As the merchant did not make any profit or loss in the entire transaction, his combined selling price of article 1 and 2 is the same as the cost price of article 1 and 2.
∴,1.22C1+0.92C2=C1+C2=600
As C1+C2=600,C2=600−C1. Substituting this in 1.22C1+0.92C2=600, we get
1.22C1+0.92(600−C1)=600
or 1.22C1−0.92C1=600−0.92×600
or 0.3C1=0.08×600=48
or C1=48(0.3)=160.
If C1=160, then C2=600−160=440.
The item that is sold at loss is article 2. The selling price of article 2=0.92×C2=0.92×440=404.80..