Question

if i sell an article for 96 rs i get a profit percentage equal to cost price.find cost price​

Answer 1

Answer:

Cost price of the article $=$ profit percent $=60$ .

Step-by-step explanation:

This question can be done by mere logic , because it is said that cost price is equal to percentage of gain.

We know that sum cost price and profit is the selling price.

So let cost price $=$ percentage of profit $=x$ ,

and profit is calculated on cost price.

Therefore here profit $=$ cost price × profit percentage

that is profit $=x*\frac{x}{100}$ .

Therefore selling price $=x+\frac{x^{2} }{100}$

                         $96=(100x+x^{2} )/100\\\\9600=x^{2} +100x$

So we get a quadratic equation $x^{2} +100x-9600 =0$

And by the method of factorization, we get two numbers  $160,-60$

such that $160+-60=100$  and  $160*-60=-9600$ .

Therefore $x^{2} +100x-9600=(x+160)(x-60)$

Thus the values of $x$ are $x=-160$  or  $x=60$ .

Since the cost price cannot be negative, the value of $x=-160$ is impossible.

Therefore $x=60$ .

Cost price of the article $=60$ rupees.

Profit percent $=60$ ,that is profit $=60*\frac{60}{100} =36$ .

Therefore selling price $=60+36=96$ .

Hence the answer is verified.

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