Two articles are sold at the same price. One at A profit of `75%` and another one at a loss of `30%`. What is the, overall profit or loss?

Options

A. `22.5%` profit
B. `57.5%` profit
C. `13(2)/7%` loss
D. none of these

Answer

To solve the problem of finding the overall profit or loss when two articles are sold at the same price, one at a profit of 75% and the other at a loss of 30%, we can follow these steps:

### Step-by-Step Solution:

1. **Let the Selling Price (SP) of each article be 'x'.**
- Since both articles are sold at the same price, we can denote the selling price of both articles as 'x'.

2. **Calculate the Cost Price (CP) of the first article (A) sold at a profit of 75%.**
- Profit Percentage = 75%
- Profit = 75% of CP = (75/100) * CP
- Therefore, Selling Price (SP) = Cost Price (CP) + Profit
- This can be written as:
\[ x = CP_A + \left(\frac{75}{100} \times CP_A\right) \]
- Simplifying this gives:
\[ x = CP_A + 0.75 \times CP_A = 1.75 \times CP_A \]
- Rearranging for CP_A:
\[ CP_A = \frac{x}{1.75} = \frac{4x}{7} \]

3. **Calculate the Cost Price (CP) of the second article (B) sold at a loss of 30%.**
- Loss Percentage = 30%
- Loss = 30% of CP = (30/100) * CP
- Therefore, Selling Price (SP) = Cost Price (CP) - Loss
- This can be written as:
\[ x = CP_B - \left(\frac{30}{100} \times CP_B\right) \]
- Simplifying this gives:
\[ x = CP_B - 0.3 \times CP_B = 0.7 \times CP_B \]
- Rearranging for CP_B:
\[ CP_B = \frac{x}{0.7} = \frac{10x}{7} \]

4. **Calculate the total Cost Price (CP) of both articles.**
- Total CP = CP_A + CP_B
- Substitute the values we found:
\[ Total\ CP = \frac{4x}{7} + \frac{10x}{7} = \frac{14x}{7} = 2x \]

5. **Determine the overall profit or loss.**
- Total Selling Price (SP) of both articles = x + x = 2x
- Total Cost Price (CP) of both articles = 2x
- Overall Profit/Loss = Total SP - Total CP = 2x - 2x = 0

Thus, the overall result is **no profit and no loss**.