Answer

Verified

366k+ 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.

Recently Updated Pages

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

Trending doubts

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

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

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

10 examples of evaporation in daily life with explanations