A merchant buys 2 articles for rs.600. He sells one of them at 22% profit and other at 8% loss and makes no profit/loss at the end what is the sp of the article that he sold at a loss?
Answers
Step-by-step explanation:
Let C
1
be the cost price of the first article and C
2
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, C
1
+C
2
=600.
The first article was sold at a profit of 22%.
∴, the selling price of the first article =C
1
+(
100
22
)C
1
=1.22C
1
The second article was sold at a loss of 8%.
∴, the selling price of the second article =C
2
−(
100
8
)C
2
=0.92C
2
.
The total selling price of the first and second article =1.22C
1
+0.92C
2
.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.
∴,1.22C
1
+0.92C
2
=C
1
+C
2
=600
As C
1
+C
2
=600,C
2
=600−C
1
. Substituting this in 1.22C
1
+0.92C
2
=600, we get
1.22C
1
+0.92(600−C
1
)=600
or 1.22C
1
−0.92C
1
=600−0.92×600
or 0.3C
1
=0.08×600=48
or C
1
=
(0.3)
48
=160.If C
1
=160, then C
2
=600−160=440.
The item that is sold at loss is article 2. The selling price of article 2=0.92×C
2
=0.92×440=404.80..