If the ratio of cost price and selling price of an article is `4 : 5`, then the percentage of profit will be

Options

A. 20
B. 0.1
C. 10
D. 25

Answer

To find the percentage of profit when the ratio of cost price (CP) to selling price (SP) is given as 4:5, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Ratios**:
- Let the cost price (CP) be represented as \( 4x \).
- Let the selling price (SP) be represented as \( 5x \).

2. **Calculate Profit**:
- Profit is calculated as the difference between selling price and cost price.
- Therefore, Profit = SP - CP = \( 5x - 4x = x \).

3. **Calculate Percentage of Profit**:
- The formula for percentage of profit is given by:
\[ \text{Percentage of Profit} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]
- Substituting the values we have:
\[ \text{Percentage of Profit} = \left( \frac{x}{4x} \right) \times 100 \]

4. **Simplify the Expression**:
- The \( x \) in the numerator and denominator cancels out:
\[ \text{Percentage of Profit} = \left( \frac{1}{4} \right) \times 100 \]
- This simplifies to:
\[ \text{Percentage of Profit} = 25 \]

5. **Final Answer**:
- Therefore, the percentage of profit is **25%**.