A person sold an article at 17.5% profit. If he would have bought it ₹ 765 less and sold it ₹ 765 less, then profit would be 22.22%, then find the original cost price of the article.

3601

Let's assume that the initial cost price of the article is Rs. x.

According to the given data, the article is sold at 17.5% profit.

Selling price of article = x + \(\frac{17.5x}{100}\)  = Rs. 1.175x

When the cost price is reduced by Rs. 765, the new cost price = Rs. x - 765

Similarly, when the selling price is reduced by Rs. 765, the new selling price = Rs. (1.175x - 765)

The profit after the decrease is 22.22%.

=> x - 765 + ( \(\frac{22.22}{100}\) ) × (x - 765) = 1.175x - 765

=> 1.175x -x =  \(\frac{22.22x - 22.22 × 765}{100}\)  

=> 0.175x × 100 = 22.22x - 16,998.3

=> 22.22x - 17.5x = 16,998.3

=> 4.72x = 16,998.3

=> x = Rs. 3601