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.

Open in App
Solution

## Let the cost price be $₹x$. First selling price $=125%$ of $x=\frac{125}{100}×x=\frac{5x}{4}$second cost price $=\left(100-20\right)%$ of $x=\frac{80}{100}×x=\frac{4x}{5}$ Second selling price will be like if it gains $30%$$=130%$ of $\frac{4x}{5}=\frac{130}{100}×\frac{4x}{5}=\frac{26x}{25}$So, by the given conditions, we have:$\frac{5x}{4}–\frac{26x}{25}=10.50\phantom{\rule{0ex}{0ex}}⇒\frac{125x-104x}{100}=10.50\phantom{\rule{0ex}{0ex}}⇒21x=1050\phantom{\rule{0ex}{0ex}}⇒x=\frac{1050}{21}\phantom{\rule{0ex}{0ex}}⇒x=50$Hence, the cost price of the article is $\mathbf{₹}\mathbf{}\mathbf{50}$.

Suggest Corrections
17
Explore more