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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 Verified Verified
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.
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