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Q.

A dealer sells an article for Rs. 75 and gains as much percent as the cost price of the article. The cost price of the article is [[1]].

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Detailed Solution

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A dealer sells an article for Rs. 75 and gains as much percent as the cost price of the article. The cost price of the article is 50.
Given that the price for which the dealer sells the article= Rs. 75.
Let the cost price of the article be Rs.

p

.
According to the given condition,
The sum of the cost price and the gain price will give us the selling price. This will help us to find the cost price. We can represent this in the equation form as,

⟹ p + (\frac{p}{100} \times p) = 75

⟹ p + \frac{p^{2}}{100} = 75

⟹ p^{2} + 100 p = 7500

⟹ p^{2} + 100 p - 7500 = 0

⟹ p^{2} + 150 p - 50 p - 7500 = 0

⟹ p (p + 150) - 50 (p + 150) = 0

⟹ (p - 50) (p + 150) = 0

⟹ p - 50 = 0 or p + 150 = 0

∴ p = 50 or p = - 150

We will choose the value

p = 50

as the cost price cannot be negative.
Therefore, the cost price of the article is Rs.50

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