Question

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

Answer 1

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

Answer: let the c. p be x

Gain = x %

S. P = C. p+ gain

S. P = 24

x + x/100= 24

100x+ x²=2400

x² + 100x - 2400=0

x²+120x-20x-2400=0

(x+120)(x-20) = 0

x = -120 ,x = 20

As cost can't have a negative value

Cost price = x = rs 20