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

$\large\boxed{\fcolorbox{blue}{yellow} {Answer}}$

The cost price of the toy is ₹ 20.

$\large\boxed{\fcolorbox{blue}{yellow} {Step - by - step explanation }}$

S. P. of the toy = ₹ 24. [Given]

Let the C. P. of the toy be ₹ x.

.°. Gain % = x %

Gain % =

$\frac{sp \: - \: cp \: }{cp} \times 100 \\ \\ = > \: x = \frac{24 - x}{x} \times 100$

$= > {x}^{2} + 100x - 2400 = 0 \\ = > {x}^{2} + 120x - 20x - 2400 = 0 \\ = > (x + 120) \: (x - 20) = 0$

.°. x + 120 = 0 or x - 20 = 0

=> x = - 120 or x = 20

As cost can't be negative,

.°. Cost price = x = ₹ 20.

Hope it helps!

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Answer 2

Answer:

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.