By selling an article for Rs96, a man gains as much percent as its cost price. Find the cost price of the article.

Answer

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

### Step 1: Define the variables
Let the cost price (CP) of the article be Rs X. The selling price (SP) is given as Rs 96.

### Step 2: Understand the relationship between profit percentage and cost price
According to the problem, the profit percentage is equal to the cost price in percentage. Therefore, if the cost price is Rs X, the profit percentage is X%.

### Step 3: Write the formula for profit percentage
The formula for profit percentage is given by:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Since the profit percentage is X%, we can write:
\[ X = \left( \frac{\text{Profit}}{X} \right) \times 100 \]

### Step 4: Express profit in terms of selling price and cost price
Profit can be expressed as:
\[ \text{Profit} = \text{SP} - \text{CP} \]
Substituting the values, we have:
\[ \text{Profit} = 96 - X \]

### Step 5: Substitute the profit in the profit percentage equation
Now we can substitute the profit into the profit percentage formula:
\[ X = \left( \frac{96 - X}{X} \right) \times 100 \]

### Step 6: Simplify the equation
Multiply both sides by X to eliminate the fraction:
\[ X^2 = (96 - X) \times 100 \]
Expanding this gives:
\[ X^2 = 9600 - 100X \]

### Step 7: Rearrange the equation
Rearranging the equation leads to:
\[ X^2 + 100X - 9600 = 0 \]

### Step 8: Factor the quadratic equation
To factor the quadratic equation, we need to find two numbers that multiply to -9600 and add to 100. The numbers are 160 and -60. Thus, we can write:
\[ (X + 160)(X - 60) = 0 \]

### Step 9: Solve for X
Setting each factor to zero gives us:
1. \(X + 160 = 0 \Rightarrow X = -160\) (not possible since cost price cannot be negative)
2. \(X - 60 = 0 \Rightarrow X = 60\)

### Conclusion
The cost price of the article is Rs 60.