By selling an article for Rs. 144, a person gained such that the percentage gain equals the cost price of the article. The cost price of the article is

Options

A. Rs.90
B. Rs.80
C. Rs.75
D. Rs.60

Answer

To find the cost price of the article, we can follow these steps:

1. **Define Variables**: Let the cost price (CP) of the article be \( X \).

2. **Understand the Gain**: The selling price (SP) of the article is given as Rs. 144. The gain is defined as the difference between the selling price and the cost price, which can be expressed as:
\[ \text{Gain} = \text{SP} - \text{CP} = 144 - X \]

3. **Set Up the Percentage Gain Equation**: The problem states that the percentage gain equals the cost price. The formula for percentage gain is:
\[ \text{Percentage Gain} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \]
Substituting the values we have:
\[ \frac{144 - X}{X} \times 100 = X \]

4. **Simplify the Equation**: Rearranging the equation gives:
\[ 144 - X = \frac{X^2}{100} \]
Multiplying through by 100 to eliminate the fraction:
\[ 100(144 - X) = X^2 \]
Expanding this gives:
\[ 14400 - 100X = X^2 \]

5. **Rearranging into Standard Form**: Rearranging the equation leads to:
\[ X^2 + 100X - 14400 = 0 \]

6. **Factoring the Quadratic Equation**: We need to factor the quadratic equation. We look for two numbers that multiply to \(-14400\) and add to \(100\). The factors are \(180\) and \(-80\):
\[ (X + 180)(X - 80) = 0 \]

7. **Finding the Roots**: Setting each factor to zero gives:
\[ X + 180 = 0 \quad \Rightarrow \quad X = -180 \quad (\text{not valid since cost price cannot be negative}) \]
\[ X - 80 = 0 \quad \Rightarrow \quad X = 80 \]

8. **Conclusion**: The cost price of the article is \( Rs. 80 \).