The ratio of the cost price and selling price of an article is 5 : 3. What is the loss percentage?

Options

A. 40
B. 20
C. 66.66
D. 33.33

Answer

To find the loss percentage when the ratio of the cost price (CP) to the selling price (SP) is given as 5:3, we can follow these steps:

### Step 1: Assign values based on the ratio
Given the ratio of CP to SP is 5:3, we can assign:
- Cost Price (CP) = 5x
- Selling Price (SP) = 3x
where x is a common multiplier.

### Step 2: Calculate the loss
Loss can be calculated using the formula:
\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} \]
Substituting the values we assigned:
\[ \text{Loss} = 5x - 3x = 2x \]

### Step 3: Calculate the loss percentage
Loss percentage is calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percentage} = \left( \frac{2x}{5x} \right) \times 100 \]

### Step 4: Simplify the expression
The x in the numerator and denominator cancels out:
\[ \text{Loss Percentage} = \left( \frac{2}{5} \right) \times 100 \]

### Step 5: Calculate the final value
Now, calculating the value:
\[ \text{Loss Percentage} = 40\% \]

Thus, the loss percentage is **40%**.

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