Question

A man sells an article at a profit of $25\%$ if he had bought it $20\%$ less and sold it for $₹10.50$ less, he would have gained $30\%$ find the cost price of the article.

Answer 1

Let the cost price be $₹x$.

First selling price $=125\%$ of $x=\frac{125}{100}\times x=\frac{5x}{4}$

second cost price $=(100-20)\%$ of $x=\frac{80}{100}\times x=\frac{4x}{5}$

Second selling price will be like if it gains $30\%$$=130\%$ of $\frac{4x}{5}=\frac{130}{100}\times \frac{4x}{5}=\frac{26x}{25}$

So, by the given conditions, we have:

$$\begin{gathered} \frac{5x}{4}–\frac{26x}{25}=10.50 \\ \Rightarrow \frac{125x-104x}{100}=10.50 \\ \Rightarrow 21x=1050 \\ \Rightarrow x=\frac{1050}{21} \\ \Rightarrow x=50 \end{gathered}$$

Hence, the cost price of the article is $\mathbf{₹}\mathbf{}\mathbf{50}$.