Question

A dealer sells an article for ₹ 75 and gains as much percent as the cost price of the article. Find the cost price of the article.

Answer 1

Let the cost price of the article be x 

∴ Gain percent x% 

According to the given condition, 

₹ x + ₹ `(x/100xx x)`

= ₹ 75 

⇒ x² + 100x = 7500

⇒ x² + 100x − 7500 = 0

⇒ x² + 150x − 5x − 7500 = 0

⇒ x (x + 150) − 50 (x + 150) = 0 

⇒ (x − 50)(x + 150) = 0 

⇒ x − 50 = 0  or  x + 150 = 0

⇒ x = 50  or  x = −150

∴ x = 50   ...(Cost price cannot be negative)

Hence, the cost price of the article is ₹ 50.