Selling price of 25 articles is equal to cost price of 20 articles. Find profit/loss percent?

Answer

To solve the problem step by step, we will follow the logic presented in the video transcript.

### Step 1: Define Variables
Let the selling price (SP) of 25 articles be equal to \( x \). Therefore, the cost price (CP) of 20 articles is also equal to \( x \).

### Step 2: Find Selling Price and Cost Price of One Article
- Selling Price of one article (SP) = \( \frac{x}{25} \)
- Cost Price of one article (CP) = \( \frac{x}{20} \)

### Step 3: Compare Selling Price and Cost Price
Since \( \frac{x}{20} > \frac{x}{25} \), we can conclude that the cost price (CP) is greater than the selling price (SP). This indicates a loss in this transaction.

### Step 4: Calculate the Loss
The formula for loss is:
\[ \text{Loss} = \text{CP} - \text{SP} \]
Substituting the values we found:
\[ \text{Loss} = \frac{x}{20} - \frac{x}{25} \]

### Step 5: Find a Common Denominator
To subtract these fractions, we need a common denominator. The least common multiple of 20 and 25 is 100. Thus, we can rewrite the fractions:
\[ \text{Loss} = \frac{5x}{100} - \frac{4x}{100} = \frac{(5x - 4x)}{100} = \frac{x}{100} \]

### Step 6: Calculate Loss Percentage
The formula for loss percentage is:
\[ \text{Loss Percent} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percent} = \left( \frac{\frac{x}{100}}{\frac{x}{20}} \right) \times 100 \]

### Step 7: Simplify the Expression
Now, simplifying the fraction:
\[ \text{Loss Percent} = \left( \frac{x}{100} \times \frac{20}{x} \right) \times 100 \]
The \( x \) cancels out:
\[ \text{Loss Percent} = \left( \frac{20}{100} \right) \times 100 = 20\% \]

### Conclusion
The loss percentage in this transaction is **20%**.

---