Question

A merchant buys two articles for Rs.600. He sells one of them at a profit of 22% and the other at a loss of 8% and makes no profit or loss in the end. What is the selling price of the article that he sold at a loss ?

Answer 1

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 $22\%$.

$\therefore$, the selling price of the first article $=C_1+\left(\frac{22}{100}\right)C_1=1.22C_1$

The second article was sold at a loss of $8\%$.

$\therefore$, the selling price of the second article $=C_2-\left(\frac{8}{100}\right)C_2=0.92C_2$.

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 $2$.

$\therefore ,1.22C_1+0.92C_2=C_1+C_2=600$

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 $1.22C_1-0.92C_1=600-0.92\times 600$

or $0.3C_1=0.08\times 600=48$

or $C_1=\frac{48}{\left(0.3\right)}=160$.

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 $2=0.92\times C_2=0.92\times 440=\mathrm{404.80.}$.