A dealer sells an article for Rs. 24 and gains as much percent as the

1.	A dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article. Find the cost price of the article.
Answer» Let the cost price be assumed as Rs x. Given, the dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article. It’s given that he gains as much as the cost price of the article, thus, Gain% = x% Gain% = \(\frac{SP - CP}{CP} \times 100\) x = \(\frac{24 - x}{x} \times 100\) ⇒ x² = (24-x) x 100 ⇒ x² + 100x – 2400 = 0 ⇒ x² + 120x – 20x – 2400 = 0 ⇒ (x + 120)(x – 20) = 0 ⇒ x = 20 or -120 Since money cannot be negative, we call neglect -120 ⇒ x = 20 Therefore, the cost price of the article is Rs 20.

A dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article. Find the cost price of the article.

Answer»

Let the cost price be assumed as Rs x.

Given, the dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article.

It’s given that he gains as much as the cost price of the article, thus, Gain% = x%

Gain% = \(\frac{SP - CP}{CP} \times 100\)

x = \(\frac{24 - x}{x} \times 100\)

⇒ x² = (24-x) x 100

⇒ x² + 100x – 2400 = 0

⇒ x² + 120x – 20x – 2400 = 0

⇒ (x + 120)(x – 20) = 0

⇒ x = 20 or -120

Since money cannot be negative, we call neglect -120

⇒ x = 20

Therefore, the cost price of the article is Rs 20.