If the profit is 10%, then what will be the ratio of cost price to selling price respectively?

Options

A. `10 : 9`
B. `10 : 11 `
C. `10 : 13 `
D. `4 : 5 `

Answer

To find the ratio of the cost price (CP) to the selling price (SP) when the profit is 10%, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Cost Price (CP)**:
Let's assume the cost price (CP) is 100. This is a convenient number to work with, as it makes calculations easier.

**Hint**: You can choose any value for CP, but using 100 simplifies the calculations.

2. **Calculate the Profit**:
Given that the profit is 10%, we can calculate the profit amount based on the cost price.
\[ \text{Profit} = 10\% \text{ of CP} = 10\% \text{ of } 100 = 10 \]

**Hint**: Remember that profit is calculated as a percentage of the cost price.

3. **Calculate the Selling Price (SP)**:
The selling price is calculated by adding the profit to the cost price.
\[ \text{Selling Price (SP)} = \text{CP} + \text{Profit} = 100 + 10 = 110 \]

**Hint**: Selling Price is always the Cost Price plus Profit.

4. **Find the Ratio of Cost Price to Selling Price**:
Now that we have both the cost price and the selling price, we can find the ratio.
\[ \text{Ratio of CP to SP} = \frac{\text{CP}}{\text{SP}} = \frac{100}{110} \]

**Hint**: Ratios can be simplified by dividing both numbers by their greatest common divisor.

5. **Simplify the Ratio**:
To simplify the ratio \( \frac{100}{110} \):
\[ \frac{100}{110} = \frac{10}{11} \]

**Hint**: Always simplify the fraction to its lowest terms for the final answer.

### Final Answer:
The ratio of the cost price to the selling price is \( \frac{10}{11} \) or 10:11.