A man sells an article at a profit of 25%. If he had bought it at 20%

1.	A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs 36.75 less, he would have gained 30%. Find the cost price of the article.
Answer» Let the cost price of article = Rs. x Profit% = 25% Selling price of article = \(x+x\times \frac{25}{100}\) = \(x+\frac{x}{4}\) = Rs. \(\frac{5x}{4}\) If CP of article is 20% less (given) Now CP becomes = \(x-x\times \frac{20}{100}\) = Rs. \(\frac{4x}{5}\) Now SP = \(\frac{5x}{4}\) - 36.75 Profit % = 30% By formula, = Gain% = \(\frac{gain}{cost\,price}\)x 100 = 30 = \(\cfrac{[(\frac{5x}{4}-36.75)-\frac{4x}{5}}{\frac{4x}{5}}\)x 100 = \(\frac{30}{100}\) x \(\frac{5}{4x}\) = \(\frac{5x-147}{4}\) - \(\frac{4x}{5}\) = \(\frac{3}{8x}\) = \(\frac{25x-588-16x}{20}\) = x = 175 Cost price of article = Rs.175

A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs 36.75 less, he would have gained 30%. Find the cost price of the article.

Answer»

Let the cost price of article = Rs. x

Profit% = 25%

Selling price of article = \(x+x\times \frac{25}{100}\) = \(x+\frac{x}{4}\) = Rs. \(\frac{5x}{4}\)

If CP of article is 20% less (given)

Now CP becomes = \(x-x\times \frac{20}{100}\) = Rs. \(\frac{4x}{5}\)

Now SP = \(\frac{5x}{4}\) - 36.75

Profit % = 30%

By formula,

= Gain% = \(\frac{gain}{cost\,price}\)x 100

= 30 = \(\cfrac{[(\frac{5x}{4}-36.75)-\frac{4x}{5}}{\frac{4x}{5}}\)x 100

= \(\frac{30}{100}\) x \(\frac{5}{4x}\) = \(\frac{5x-147}{4}\) - \(\frac{4x}{5}\)

= \(\frac{3}{8x}\) = \(\frac{25x-588-16x}{20}\) = x = 175

Cost price of article = Rs.175