Question

A girl sold her pen for Rs. 39 and got a percentage of profit numerically equal to the cost price. The cost price of that pen is:
(a) 130
(b) 90
(c) 60
(d) 30

Answer 1

Hint: If we properly interpret the question, we will find that it is given that the selling price of the pen is equal to cost price added with the profit, i.e., cost price percent of the cost price, as it is given that cost price and percentage profit are numerically equal. So, represent this mathematically and equate it with Rs. 39 and solve the quadratic equation you get using the quadratic formula to get the answer.

Complete step-by-step answer:
Let us try to interpret the meaning of the statement given in the question. If we interpret we will find that it is given that the selling price of the pen is equal to the cost price added with the profit, i.e., cost price percent of the cost price, as it is given that cost price and percentage profit are numerically equal. So, let the CP of the pen to be x.
$selling\text{ }price=\ cost\text{ }price\text{ }+\text{ }profit.$
$\Rightarrow selling\text{ }price=x\text{ }+\text{ }\dfrac{x}{100}\times x$
It is also given that the selling price of the pen was Rs. 39. So, if we put this in the equation, we get
$39=x\text{ }+\text{ }\dfrac{{{x}^{2}}}{100}$
$\Rightarrow \dfrac{{{x}^{2}}+100x}{100}=39$
$\Rightarrow {{x}^{2}}+100x-3900=0$
Now we will find the values of x that satisfies the above quadratic equation. For finding we will use the quadratic formula.
$x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}=\dfrac{-100\pm \sqrt{{{100}^{2}}+4\times 1\times 3900}}{2}=\dfrac{-100\pm \sqrt{25600}}{2}$
Now we know that CP is positive, so $x=\dfrac{-100+\sqrt{25600}}{2}$ is the only acceptable value and the root of 25600 is 160.
$x=\dfrac{-100+160}{2}=30$
Therefore, the answer to the above question is option (d).

Note: The easiest method to solve this question is by option elimination. If you see that there is only one option which is less than the selling price and selling price is always more than the cost price, until and unless a loss is mentioned in the question. So, option (d) is only the possible option so it is the answer.