A person sells an article for $ 75 and gains as much percent

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A person sells an article for $ 75 and gains as much percent as the cost price of the article in rupees. The cost price of the article is

1. $ 37.50
2. $ 40
3. $ 50
4. $ 150

Correct Option: C

Let the cost price be y
∴ Gain % = y%
∴ S.P. = C.P. + y% of C.P

⇒ 75 = y +	y²
	100

⇒ y ² + 100y – 7500 = 0
⇒ y² + 150y – 50y – 7500 = 0
⇒ y (y + 150) – 50 (y + 150) = 0
⇒ (y + 150) (y – 50) = 0
⇒ y = $ 50 [as y cannot be negative]
Therefore , The cost price of the article is $ 50 .