Question

9. By selling an article for Rs. 56, a man gains as much percentage as the cost price is, Find the cost
price?​

Answer 1

Given:

Selling price of an article = Rs. 56

Cost price = Gain percentage

To find:

The cost price of the article

Solution:

Let "x" represent the cost price of the article.

∴ Gain percentage will also be "x%"

We know the formula to find the gain percentage is as follows:

$\boxed{\boxed{\bold{Gain\% = \frac{Gain }{C.P.} \times100= \frac{(S.P. - C.P.) }{C.P.}\times100}}}$

Now, substituting the values of  Gain% = C.P. = x and S.P. = 56 in the above formula, we get

$x = \frac{(56 - x) }{x}\times100$

⇒ $x^2 = (56 - x) \times 100$

⇒ $x^2 = 5600 - 100x$

⇒ $x^2 + 100x - 5600 = 0$

⇒ $x^2 + 140x - 40x - 5600 = 0$

⇒ $x(x + 140) - 40(x + 140) = 0$

⇒ $(x + 140) (x - 40) = 0$

⇒ $x = -140 \:or\: 40$

price or percentage cannot be negative so, we will discard the negative value  

⇒ $\bold{x = 40}$

Thus, the cost price of the article is Rs. 40.

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