If a man estimates his loss as 20% of the selling price, then his loss per cent is:

Options

A. 0.2
B. 0.25
C. `40/3` %
D. `50/3` %

Answer

To find the actual loss percent when a man estimates his loss as 20% of the selling price (SP), we can follow these steps:

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Loss
- The loss is calculated as a percentage of the Cost Price (CP), not the Selling Price (SP).
- The relationship can be expressed as:
\[ \text{Loss} = \text{CP} - \text{SP} \]

### Step 2: Define the Selling Price in terms of Loss
- According to the problem, the man estimates his loss as 20% of the Selling Price.
- Therefore, if we let the Selling Price (SP) be \( x \), then:
\[ \text{Loss} = 20\% \text{ of } x = \frac{20}{100} \times x = 0.2x \]

### Step 3: Relate Selling Price to Cost Price
- From the relationship of SP and CP, we can express CP in terms of SP and Loss:
\[ \text{CP} = \text{SP} + \text{Loss} \]
- Substituting the loss we found:
\[ \text{CP} = x + 0.2x = 1.2x \]

### Step 4: Calculate the Actual Loss
- The actual loss can now be expressed as:
\[ \text{Loss} = \text{CP} - \text{SP} = 1.2x - x = 0.2x \]

### Step 5: Calculate the Actual Loss Percentage
- The actual loss percentage is calculated using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \]
- Substituting the values we have:
\[ \text{Loss Percentage} = \left( \frac{0.2x}{1.2x} \right) \times 100 \]
- The \( x \) cancels out:
\[ \text{Loss Percentage} = \left( \frac{0.2}{1.2} \right) \times 100 = \frac{20}{12} \times 100 = \frac{500}{3} \approx 16.67\% \]

### Final Answer
- The actual loss percentage is \( \frac{50}{3}\% \).

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