Question

A dealer sells a toy for RS.24 and gains as much percent as the cost price of the toy. Find the cost price of the toy.​

Answer 1

Step-by-step explanation:

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.

Answer 2

$\huge\underline\mathbb{SOLUTION:-}$

$\mathsf {Let, \: the \: C.P \: be \: x.}$

$\therefore \mathsf {Gain = x\%}$

$\implies \mathsf {x\% = \frac{x}{100}}$

$\mathsf {S.P = C.P + Gain}$

$\mathsf {S.P = 24}$

$\implies \mathsf {x + \frac{x {}^{2} }{100} = 24}$

$\mathsf {On \: solving \: x = 20 \: or \: - 120(rej)}$

$\therefore \mathsf \blue{C.P \: of \: toy = RS.20}$