If a person gets loss of 20% on his selling price, then the loss percent is

Options

A. `20%`
B. `25%`
C. `40/3`%
D. `50/3`%

Answer

To solve the problem step by step, we need to find the loss percent when a person incurs a loss of 20% on his selling price.

### Step 1: Understand the relationship between Cost Price (CP), Selling Price (SP), and Loss
- Let the Selling Price (SP) be represented as \( SP = 100x \) (where \( x \) is a variable).
- Given that the person incurs a loss of 20% on the Selling Price, we can express the loss in terms of \( x \).

### Step 2: Calculate the Loss
- Since the loss is 20% of the Selling Price, we can calculate the loss:
\[ \text{Loss} = 20\% \text{ of } SP = \frac{20}{100} \times SP = \frac{20}{100} \times 100x = 20x \]

### Step 3: Determine the Cost Price (CP)
- The Cost Price (CP) can be calculated using the formula:
\[ CP = SP + \text{Loss} \]
- Substituting the values we have:
\[ CP = 100x + 20x = 120x \]

### Step 4: Calculate the Loss Percentage
- The formula for loss percentage is given by:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{CP} \right) \times 100 \]
- Substituting the values of Loss and CP:
\[ \text{Loss Percentage} = \left( \frac{20x}{120x} \right) \times 100 \]

### Step 5: Simplify the Expression
- Simplifying the fraction:
\[ \text{Loss Percentage} = \left( \frac{20}{120} \right) \times 100 = \left( \frac{1}{6} \right) \times 100 \]
- This further simplifies to:
\[ \text{Loss Percentage} = \frac{100}{6} \approx 16.67\% \]

### Final Answer
The loss percentage is approximately **16.67%**.

---