An article is sold at 5% profit. The ratio of selling price and cost price will be

Options

A. `1:5`
B. `20:21`
C. `21:20`
D. `5:1`

Answer

To find the ratio of Selling Price (SP) to Cost Price (CP) when an article is sold at a 5% profit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Cost Price (CP): The price at which an article is purchased.
- Selling Price (SP): The price at which an article is sold.
- Profit Percentage: The percentage of profit made on the Cost Price.

2. **Use the Profit Formula**:
- The formula to calculate Selling Price when profit percentage is known is:
\[ SP = CP \times \left(1 + \frac{\text{Profit Percentage}}{100}\right) \]
- In this case, the profit percentage is 5%.

3. **Substitute the Profit Percentage**:
- Substitute the profit percentage into the formula:
\[ SP = CP \times \left(1 + \frac{5}{100}\right) \]
- Simplifying this gives:
\[ SP = CP \times \left(1 + 0.05\right) = CP \times 1.05 \]

4. **Find the Ratio of SP to CP**:
- To find the ratio of Selling Price to Cost Price, we can express it as:
\[ \frac{SP}{CP} = \frac{CP \times 1.05}{CP} \]
- The CP cancels out:
\[ \frac{SP}{CP} = 1.05 \]

5. **Convert to Fraction**:
- The ratio 1.05 can be expressed as a fraction:
\[ 1.05 = \frac{105}{100} = \frac{21}{20} \]

6. **Final Ratio**:
- Therefore, the ratio of Selling Price to Cost Price is:
\[ SP : CP = 21 : 20 \]

### Conclusion:
The ratio of Selling Price to Cost Price when an article is sold at a 5% profit is **21:20**.