Question

A dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article. Find the cost price of the article.

Answer 1

SOLUTION :  

Let the cost price (C.P) of an article be ₹ x.

Gain % = cost price (C.P)

Gain % =  x

Gain(profit) = ( Gain % × CP)/100

Gain(profit) = ₹ (x × x) /100

Gain= ₹ x²/100

SP = C.P + Gain

24 = x  + x²/100     [Given, S.P = ₹ 24]

(100x + x² /100) = 24

100x + x² = 24×100

x² +100x = 2400

x² +100x - 2400 = 0

x² +120x -20x -2400 = 0

[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

Cost price of an article  can't be negative. So x ≠ -120. Therefore, x = 20

Hence, the cost price of an article is ₹ 20.

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Answer 2

Question :

A dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article. Find the cost price of the article.

Answer:

Cost price is Rs 20

Step-by-step explanation:

Let the C.P be x .

Gain % =  gain / C.P × 100

⇒ Gain % = gain / x × 100

Gain % = x

⇒ x = gain / x × 100

⇒ x² / 100 = gain .

We know that SP = C.P + Gain

24 = x  + x²/100

⇒ ( 100 x + x² ) / 100 = 24  

⇒ (100 x + x² /100) = 24

⇒ 100 x + x² = 2400

⇒ x² +100 x - 2400 = 0

⇒ x² +120 x -20 x -2400 = 0

⇒ x ( x + 120 ) -20 ( x + 120 ) = 0

⇒ ( x  - 20 ) ( x + 120 ) = 0

Either :

(x -20)  = 0  

Or

(x +120)= 0

Either

x = 20  

or

x= -120

x cannot be negative .

Hence, the cost price of an article is ₹ 20.