Question

A pen is sold for rs11 and makes the same percentage of profit for which it was purchased. Find its purchase price​

Answer 1

Answer:

The purchase price is Rs. 10.

Step-by-step explanation:

Let the purchase (cost) price of the pen be Rs. x.

The selling price is Rs. 11.

The profit percentage is x%.

The formula for selling price is: $SP=CP[1+\frac{Profit}{100}]$

Determine the value of x as follows:

$SP=CP[1+\frac{Profit}{100}]\\11=x[1+\frac{x}{100}]\\1100=100x+x^{2}\\x^{2}+100x-1100=0$

The resultant equation is a quadratic equation.

The roots of a quadratic equation are: $x=\frac{-b\pm\sqrt{b^{2}-4ac} }{2a}$

Here a = 1, b = 100 and c = -1100

The roots are:

$x=\frac{-100\pm\sqrt{100^{2}-(4\times1\times-1100)} }{2\times1}=\frac{-100\pm 120}{2}=(\frac{-100- 120}{2},\frac{-100+ 120}{2}) =(-110, 10)$

Since denotes the cost of a article it cannot be negative,

The value of x is 10.

Thus, the purchase price is Rs. 10.