Loss % on selling an article for Rs 50 is equal to the profit % on selling the same article for Rs 70 . Find profit/loss %.

Answer

To solve the problem, we need to find the cost price (CP) of the article and then determine the profit and loss percentages based on the selling prices (SP) given.

### Step-by-Step Solution:

1. **Define the Selling Prices (SP):**
- Selling Price 1 (SP1) = Rs 50 (where there is a loss)
- Selling Price 2 (SP2) = Rs 70 (where there is a profit)

2. **Understand the Relationship:**
- According to the problem, the loss percentage when selling at Rs 50 is equal to the profit percentage when selling at Rs 70.

3. **Set Up the Equations:**
- Let the Cost Price (CP) be Rs x.
- Loss when selling for Rs 50:
\[ \text{Loss} = CP - SP1 = x - 50 \]
- Profit when selling for Rs 70:
\[ \text{Profit} = SP2 - CP = 70 - x \]

4. **Express Loss and Profit in Terms of Percentages:**
- Loss Percentage when selling for Rs 50:
\[ \text{Loss Percentage} = \left(\frac{x - 50}{x}\right) \times 100 \]
- Profit Percentage when selling for Rs 70:
\[ \text{Profit Percentage} = \left(\frac{70 - x}{x}\right) \times 100 \]

5. **Set the Loss Percentage Equal to the Profit Percentage:**
\[ \frac{x - 50}{x} \times 100 = \frac{70 - x}{x} \times 100 \]
- We can cancel 100 from both sides:
\[ \frac{x - 50}{x} = \frac{70 - x}{x} \]

6. **Cross-Multiply to Solve for CP (x):**
\[ (x - 50) = (70 - x) \]
- Rearranging gives:
\[ x - 50 + x = 70 \]
\[ 2x = 120 \]
\[ x = 60 \]

7. **Calculate Loss Percentage:**
- Loss when selling for Rs 50:
\[ \text{Loss} = 60 - 50 = 10 \]
- Loss Percentage:
\[ \text{Loss Percentage} = \left(\frac{10}{60}\right) \times 100 = \frac{1000}{60} = 16.67\% \text{ (or } 16\frac{2}{3}\% \text{)} \]

8. **Calculate Profit Percentage:**
- Profit when selling for Rs 70:
\[ \text{Profit} = 70 - 60 = 10 \]
- Profit Percentage:
\[ \text{Profit Percentage} = \left(\frac{10}{60}\right) \times 100 = \frac{1000}{60} = 16.67\% \text{ (or } 16\frac{2}{3}\% \text{)} \]

### Conclusion:
- The loss percentage when selling for Rs 50 is 16.67% (or 16⅔%).
- The profit percentage when selling for Rs 70 is also 16.67% (or 16⅔%).