If the loss percent on an article is 30%, then what is the ratio of the cost price and selling price?

Options

A. `10:13`
B. `13:10`
C. `7:10`
D. `10:7`

Answer

To solve the problem of finding the ratio of the cost price (CP) and selling price (SP) when there is a 30% loss, we can follow these steps:

### Step 1: Understand the loss percentage formula
The loss percentage is calculated using the formula:
\[ \text{Loss Percentage} = \frac{\text{Loss}}{\text{Cost Price}} \times 100 \]
Given that the loss percentage is 30%, we can express this as:
\[ 30 = \frac{\text{Loss}}{\text{CP}} \times 100 \]

### Step 2: Express the loss in terms of CP and SP
The loss can also be expressed as:
\[ \text{Loss} = \text{CP} - \text{SP} \]
Substituting this into the loss percentage formula gives:
\[ 30 = \frac{\text{CP} - \text{SP}}{\text{CP}} \times 100 \]

### Step 3: Simplify the equation
Rearranging the equation, we get:
\[ \frac{\text{CP} - \text{SP}}{\text{CP}} = \frac{30}{100} = \frac{3}{10} \]
This can be rewritten as:
\[ \text{CP} - \text{SP} = \frac{3}{10} \text{CP} \]

### Step 4: Rearranging the terms
Now, we can rearrange the equation:
\[ \text{CP} - \frac{3}{10} \text{CP} = \text{SP} \]
This simplifies to:
\[ \frac{7}{10} \text{CP} = \text{SP} \]

### Step 5: Finding the ratio of CP to SP
To find the ratio of CP to SP, we can express it as:
\[ \frac{\text{CP}}{\text{SP}} = \frac{\text{CP}}{\frac{7}{10} \text{CP}} = \frac{10}{7} \]

### Conclusion
Thus, the ratio of the cost price to the selling price is:
\[ \text{CP : SP} = 10 : 7 \]

### Final Answer
The answer is option D: 10 is to 7.

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