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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.
Solution
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.
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