By selling an article for 21, a man lost such that the percentage loss was equal to the cost price. The cost price of the article is :

Answer

To solve the problem, we need to find the cost price (CP) of the article given that the selling price (SP) is 21 and the percentage loss is equal to the cost price. Let's denote the cost price as CP.

### Step-by-Step Solution:

1. **Understanding the Loss**:
The problem states that the percentage loss is equal to the cost price. If we denote the percentage loss as P%, then we have:
\[ P = CP \]

2. **Formula for Percentage Loss**:
The formula for percentage loss is given by:
\[ \text{Percentage Loss} = \frac{\text{Loss}}{\text{Cost Price}} \times 100 \]
The loss can also be expressed as:
\[ \text{Loss} = CP - SP \]
Substituting this into the percentage loss formula gives us:
\[ P = \frac{CP - SP}{CP} \times 100 \]

3. **Substituting Known Values**:
We know that the selling price (SP) is 21. Therefore, we can substitute this into the equation:
\[ CP = \frac{CP - 21}{CP} \times 100 \]

4. **Rearranging the Equation**:
To eliminate the fraction, we can multiply both sides by CP:
\[ CP^2 = (CP - 21) \times 100 \]
Expanding the right side:
\[ CP^2 = 100CP - 2100 \]

5. **Forming a Quadratic Equation**:
Rearranging gives us:
\[ CP^2 - 100CP + 2100 = 0 \]

6. **Using the Quadratic Formula**:
We can solve this quadratic equation using the quadratic formula:
\[ CP = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Here, \(a = 1\), \(b = -100\), and \(c = 2100\):
\[ CP = \frac{100 \pm \sqrt{(-100)^2 - 4 \times 1 \times 2100}}{2 \times 1} \]
\[ CP = \frac{100 \pm \sqrt{10000 - 8400}}{2} \]
\[ CP = \frac{100 \pm \sqrt{1600}}{2} \]
\[ CP = \frac{100 \pm 40}{2} \]

7. **Calculating the Values**:
This gives us two potential solutions:
\[ CP = \frac{140}{2} = 70 \quad \text{or} \quad CP = \frac{60}{2} = 30 \]

8. **Choosing the Correct Value**:
Since the percentage loss cannot be greater than the cost price, we take the lower value:
\[ CP = 30 \]

### Final Answer:
The cost price of the article is **30**.