a dealer sells an article for Rs 24 and gains as much as percentage of cost price of the article find the cost of the article
Answers
Question: A dealer sells an article for Rs 24 and gains as much as percentage of cost price of the article find the cost of the article.
To find: We have to find the cost of article.
Answer: Cost price of article is Rs 20.
Step by step explanation:
Let the cost price of article be x.
It is given that, Cost Price (C.P) = Gain %
Gain % = x
Gain profit = Gain % × CP/100
Gain profit = x × x / 100
Gain profit = x²/100
Selling price of Article = Cost Price + Gain profit
But, Selling price = 24
24 = x²/100
100x + x²/100 = 24
100x + x² = 24 × 100
x² +100x = 2400
x² +100x - 2400 = 0
x² +120x -20x -2400 = 0
We can now split the middle term. Therefore, By middle term splitting:
x(x + 120) -20(x + 120) = 0
(x -20) (x +120)= 0
(x -20) = 0 or (x +120)= 0
x = 20 or x= -120
As we know that, Cost price of article can't be negative. Therefore, X ≠ 120.
Hence, Cost price of article is 20 Rs.