If the loss per cent on an article is 15%, then the ratio of the cost price and the selling price will be :

Options

A. `17:20`
B. `20:17`
C. `23:15`
D. `15:23`

Answer

To solve the problem, we need to find the ratio of the cost price (CP) to the selling price (SP) when there is a loss of 15%. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Loss Percentage
We are given that the loss percentage on an article is 15%. This means that the selling price is less than the cost price.

### Step 2: Assume a Cost Price
Let’s assume the cost price (CP) of the article is 100 units (this can be in any currency, but for simplicity, we will use 100).

### Step 3: Calculate the Selling Price
To find the selling price (SP) when there is a loss, we can use the formula:
\[ \text{SP} = \text{CP} - \text{Loss} \]
Since we have a loss of 15%, we can express it as:
\[ \text{Loss} = \frac{15}{100} \times \text{CP} \]
Substituting the assumed value of CP:
\[ \text{Loss} = \frac{15}{100} \times 100 = 15 \]
Now, substituting this back into the SP formula:
\[ \text{SP} = 100 - 15 = 85 \]

### Step 4: Find the Ratio of CP to SP
Now that we have both CP and SP, we can find the ratio:
\[ \text{Ratio of CP to SP} = \frac{\text{CP}}{\text{SP}} = \frac{100}{85} \]

### Step 5: Simplify the Ratio
To simplify the ratio \( \frac{100}{85} \), we can divide both the numerator and the denominator by 5:
\[ \frac{100 \div 5}{85 \div 5} = \frac{20}{17} \]

### Final Answer
Thus, the ratio of the cost price to the selling price is:
\[ \text{Ratio} = 20 : 17 \]

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