Question

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

Answer 1

Answer:

Let the cost price of the toy be Rs. x.

Then gain x% Gain Rs.(x×  

100

x

​  

)=Rs.  

100

x  

2

 

​  

 

S.P=C.P+Gain =x+  

100

x  

2

 

​  

 

But S.P=Rs.24

⇒x+  

100

x  

2

=24

⇒100x+x  

2

=2400⇒x  

2

+100x−2400=0

⇒x  

2

+120x−20x−2400=0⇒x(x+120)−20(x+120)=0

⇒(x+120)(x−20)=0⇒x=20,−120⇒x=20

Hence the cost price of the toy is Rs. 20

Answer 2

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

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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