Question

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

Answer 1

Let the cost price of the toy be ₹ x.
Gain =  x %
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
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 of toy  can't be negative.So x = 20.

Hence, the cost price of the toy is ₹ 20.

HOPE THIS WILL HELP YOU...

Answer 2

Hey



SP = Rs 24


Let CP be Rs x .


So ,


Gain% = x % .


Now ,


x + x % of x = SP


=> x + x / 100 * x = 24


=> x + x² / 100 = 24


=> 100x + x² = 2400


=> x ² + 100x - 2400 = 0



D = ( 100 ) ² - 4 * ( - 2400 )



= 10000 + 9600

= 19600


So , √D = 140


Now ,


x = -( b ) ± √D / 2a


= -100 + 140 / 2


= 40 / 2


= 20


So ,

CP = Rs 20

and gain% = 20%


thanks :)