Question

A dealer sells a toy for Rs. 24 and gains as much percent as the cost price of the toy, then cost price of the toy is...

Answer 1

SP=24/-

Given, profit%=CP=x

We know that,

$profit \: percentage = profit \div costprice \times 100$

Profit =SP-CP

Profit=24-x

So,

$x = \frac{24 - x}{x} \times 100 \\ {x}^{2} = 2400 - 100x \\ {x}^{2} + 100x - 2400 = 0 \\ {x}^{2} + 120x - 20x - 2400 = 0 \\ x(x + 120) - 20(x + 120) = 0 \\ (x + 120)(x - 20) = 0$

Implies, x=-120 or x=20

Since price can't be - ve, x=20

Therefore, costprice=20/-

PLEASE MARK IT AS BRAINLIEST...

Answer 2

CP is the cost price.

Gain% =  CP%

 Gain or profit = CP * CP/100

SP = CP + profit = CP + CP²/100  = 24

CP² + 100 CP - 2400 = 0 

 CP = [ -100 +- √(10,000 + 9, 600) ] /2 

    =  20   taking only the positive  value.

So Rs 20 is the cost price and 20% is the gain.

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CP² + 100 CP - 2, 400 = 0

(CP - 20) ( CP ( + 1200) = 0   So CP = 20.