**Q) A dealer sells an article for Rs. 75 and gains as much percent as the cost price of the article. Find the cost price of the article.**

**Ans: **Let’s consider the cost price of the article is X

At sales price of Rs. 75, his profit is 75 – X

The percentage % gain is x 100

By given condition, % gain = Cost price

∴ x 100 = X

∴ 100 (75 – X) = X 2

∴ X2 + 100 X – 7500 = 0

∴ X2 + 100 X – 7500 = 0 5 x 5 x 5 x 5 x 3 x 2 x 2

∴ X2 + 150 X – 50 X – 7500 = 0

∴ X(X + 150) – 50 (X + 150) = 0

∴ (X + 150) (X – 50) = 0

∴ X = 50 and X = – 150

Here, we reject X = – 150 because the cost price of an article can never be negative.

∴ X = 50

**Therefore, the cost price of the article is Rs. 50.**

**Check:** At cost of Rs. 50 and Saale price of Rs. 75, profit is Rs. 25

*Hence, % profit = = 50%*

*It satisfies the given condition, hence our answer is correct.*

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