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
261k+ views
Hint – In order to solve this problem assume the cost price and make the equation by applying the formula of cost price.
It is given that the selling price of an article is Rs.24.
Let the cost price of the article be Rs. x. ……(i)
Then according to the question the percent the dealer gets is x%.
The profit is x%.
We know that the formula for total gain is :
${\text{Cost price }} \times {\text{ }}\dfrac{{{\text{gain}}}}{{100}} = {\text{x }} \times {\text{ }}\dfrac{{\text{x}}}{{100}} = \dfrac{{{{\text{x}}^2}}}{{100}}$ ……(ii)
We also know ,
Cost price = selling price – profit (gain)
${\text{x}}$= 24 - $\dfrac{{{{\text{x}}^2}}}{{100}}$ ……[From (i) and (ii)]
$100{\text{x = 2400 - }}{{\text{x}}^2}$
On solving further we get,
${{\text{x}}^2} + 100{\text{x - 2400 = 0}}$
Then solving by splitting the middle term we get,
$
{{\text{x}}^2} - 20{\text{x + 120x - 2400 = 0}} \\
{\text{x(x - 20)}}\,\,\, + \,\,120{\text{(x - 20) = 0}} \\
({\text{x + 120}})({\text{x - 20}}) = 0 \\
$
Then, either x = 20 or x = -120
But as x is cost price it cannot be negative
Therefore, x = -120 will be neglected.
Then the value of x = 20.
Hence the cost price of the toy is Rs.20.
Note – In these type of questions of getting the cost price of the item if the selling price is given and percentage of profit is also given same as the cost price , so , here we have made the equations by assuming the variable for cost price and then used the formula of cost price that is cost price = selling price – profit . We got a quadratic equation in one variable as the percentage of profit is the same as that of cost price. After solving it by splitting the middle term we got the cost price of the item.
It is given that the selling price of an article is Rs.24.
Let the cost price of the article be Rs. x. ……(i)
Then according to the question the percent the dealer gets is x%.
The profit is x%.
We know that the formula for total gain is :
${\text{Cost price }} \times {\text{ }}\dfrac{{{\text{gain}}}}{{100}} = {\text{x }} \times {\text{ }}\dfrac{{\text{x}}}{{100}} = \dfrac{{{{\text{x}}^2}}}{{100}}$ ……(ii)
We also know ,
Cost price = selling price – profit (gain)
${\text{x}}$= 24 - $\dfrac{{{{\text{x}}^2}}}{{100}}$ ……[From (i) and (ii)]
$100{\text{x = 2400 - }}{{\text{x}}^2}$
On solving further we get,
${{\text{x}}^2} + 100{\text{x - 2400 = 0}}$
Then solving by splitting the middle term we get,
$
{{\text{x}}^2} - 20{\text{x + 120x - 2400 = 0}} \\
{\text{x(x - 20)}}\,\,\, + \,\,120{\text{(x - 20) = 0}} \\
({\text{x + 120}})({\text{x - 20}}) = 0 \\
$
Then, either x = 20 or x = -120
But as x is cost price it cannot be negative
Therefore, x = -120 will be neglected.
Then the value of x = 20.
Hence the cost price of the toy is Rs.20.
Note – In these type of questions of getting the cost price of the item if the selling price is given and percentage of profit is also given same as the cost price , so , here we have made the equations by assuming the variable for cost price and then used the formula of cost price that is cost price = selling price – profit . We got a quadratic equation in one variable as the percentage of profit is the same as that of cost price. After solving it by splitting the middle term we got the cost price of the item.
Last updated date: 21st Sep 2023
•
Total views: 261k
•
Views today: 3.61k
Recently Updated Pages
What do you mean by public facilities

Paragraph on Friendship

Slogan on Noise Pollution

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

10 Slogans on Save the Tiger

Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The equation xxx + 2 is satisfied when x is equal to class 10 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Drive an expression for the electric field due to an class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

What is the past tense of read class 10 english CBSE
