20% loss on selling price is what per cent loss on the cost price ?

Options

A. a) `25%`
B. b) `15%`
C. c) `16(2)/(3)%`
D. d) `16(1)/(3)%`

Answer

To solve the problem of finding out what percentage loss on the cost price corresponds to a 20% loss on the selling price, we can follow these steps:

### Step-by-Step Solution:

1. **Define Selling Price (SP)**:
Let's assume the Selling Price (SP) is 100.

2. **Calculate Loss**:
Since there is a 20% loss on the Selling Price, the loss amount can be calculated as:
\[ \text{Loss} = 20\% \text{ of SP} = 20\% \text{ of } 100 = 20. \]

3. **Calculate Cost Price (CP)**:
The Cost Price (CP) can be calculated using the formula:
\[ \text{CP} = \text{SP} + \text{Loss} = 100 + 20 = 120. \]

4. **Calculate Loss Percentage on Cost Price**:
Now, we need to find the loss percentage based on the Cost Price. The formula for loss percentage is:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100. \]
Substituting the values we have:
\[ \text{Loss Percentage} = \left( \frac{20}{120} \right) \times 100. \]

5. **Simplify the Calculation**:
Simplifying the fraction:
\[ \frac{20}{120} = \frac{1}{6}. \]
Therefore,
\[ \text{Loss Percentage} = \frac{1}{6} \times 100 = \frac{100}{6} \approx 16.67. \]

6. **Convert to Mixed Fraction**:
The decimal 16.67 can be expressed as a mixed fraction:
\[ 16 \frac{2}{3}. \]

### Final Answer:
Thus, a 20% loss on the selling price corresponds to a loss of **16⅔%** on the cost price.