Question

Rahul sold an article for Rs 56 which cost him Rs $x$. He finds that he gained $x\%$ on his outlay. Find $x$.

Answer 1

Step 1: Given information in the question.

The cost price of an article is Rs $x$.

The selling price of an article is $\text{Rs}.56$.

The gain $\%$ of the article is $x\%$.

Step 2: Use the formula of gain percent.

$\begin{array}{rcl}\text{Gain}\%& =& \frac{S.P-C.P}{C.P}\times 100\\ x& =& \frac{56-x}{x}\times 100\\ x^2& =& 5600-100x\\ x^2+100x-5600& =& 0\end{array}$

Step 3: Factorise the obtained quadratic equation.

$\begin{array}{rcl}{x}^2+100x-5600& =& 0\\ x^2+140x-40x-5600& =& 0\\ x\left(x+140\right)-40\left(x-140\right)& =& 0\\ \left(x+140\right)\left(x-40\right)& =& 0\\ x& =& -140\text{or}40\end{array}$

Neglect the negative value because the price can not be negative.

Hence, the value of $x$ is $40$.