The ratio between the sale price and the cost price of an article is `7 :5.` What ratio between the profit and the cost price of that article ?

Options

A. `2:5
B. `5:2`
C. `7:2`
D. 0.086805555555556

Answer

To solve the problem, we need to find the ratio between the profit and the cost price of an article, given that the ratio between the sale price (SP) and the cost price (CP) is 7:5.

### Step-by-Step Solution:

1. **Define the Ratios**:
- Let the cost price (CP) be represented as \( 5x \).
- Since the ratio of sale price (SP) to cost price (CP) is 7:5, we can represent the sale price as \( 7x \).

2. **Calculate Profit**:
- Profit is calculated as:
\[ \text{Profit} = \text{Sale Price} - \text{Cost Price} = SP - CP \]
- Substituting the values we have:
\[ \text{Profit} = 7x - 5x = 2x \]

3. **Find the Ratio of Profit to Cost Price**:
- Now, we need to find the ratio of profit to cost price:
\[ \text{Ratio of Profit to Cost Price} = \frac{\text{Profit}}{\text{Cost Price}} = \frac{2x}{5x} \]
- Simplifying this gives:
\[ \frac{2x}{5x} = \frac{2}{5} \]

4. **Final Answer**:
- Therefore, the ratio between the profit and the cost price of the article is \( 2:5 \).