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.

Question

Philoid · Accepted Answer

Let the cost price be Rs a.

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% = a%

Gain% = $\frac{SP-CP}{CP}\times100$

⇒ $a = \frac{24-a}{a}\times100$

⇒ a² = (24-a) $\times$ 100

⇒ a² + 100a – 2400 = 0

⇒ a² + 120a – 20a – 2400 = 0

⇒ (a + 120)(a – 20) = 0

⇒ a = 20 or -120

Since money cannot be negative so, negalecting -120, we get,

⇒ a = 20

Thus, the cost price of the article is Rs 20