Loss of 20% on selling price is equal to x% loss on cost price. What is the value of x?

Options

A. 20
B. 25
C. 16 `2/3`
D. 16

Answer

To solve the problem, we need to find the value of \( x \) such that a loss of 20% on the selling price (SP) is equal to \( x\% \) loss on the cost price (CP).

### Step-by-step Solution:

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

2. **Calculate the Loss on Selling Price**:
The loss is given as 20% of the Selling Price. Therefore, the loss can be calculated as:
\[ \text{Loss} = 20\% \text{ of } SP = \frac{20}{100} \times SP = \frac{1}{5} \times SP \]

3. **Determine the Cost Price (CP)**:
The Cost Price (CP) can be expressed in terms of SP and the loss:
\[ CP = SP + \text{Loss} = SP + \frac{1}{5} SP = SP \left(1 + \frac{1}{5}\right) = SP \left(\frac{5}{5} + \frac{1}{5}\right) = SP \left(\frac{6}{5}\right) \]

4. **Express SP in terms of CP**:
Rearranging the equation gives:
\[ SP = \frac{5}{6} CP \]

5. **Calculate the Loss on Cost Price**:
Now, we need to find the loss percentage on the Cost Price (CP). The loss is still \( \frac{1}{5} SP \), which we can substitute:
\[ \text{Loss on CP} = \frac{1}{5} SP = \frac{1}{5} \left(\frac{5}{6} CP\right) = \frac{1}{6} CP \]

6. **Calculate the Loss Percentage**:
The loss percentage on CP can be calculated as:
\[ \text{Loss Percentage} = \left(\frac{\text{Loss}}{CP}\right) \times 100\% = \left(\frac{\frac{1}{6} CP}{CP}\right) \times 100\% = \frac{1}{6} \times 100\% = \frac{100}{6}\% = 16\frac{2}{3}\% \]

7. **Conclusion**:
Therefore, \( x = 16\frac{2}{3}\% \).

### Final Answer:
The value of \( x \) is \( 16\frac{2}{3}\% \).

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