If a discount of 10% is allowed on the marked price of an article, a shopkeeper gets a profit of 25%. If he offers a discount of 25% on the marked price of the same article, then his percentage profit `//`loss will be `:`

Options

A. `4 ( 1)/( 6)` profit
B. `4%` loss
C. `4 ( 1)/( 6) %` loss
D. `4% `profit

Answer

To solve the problem step by step, we need to analyze the situation involving the marked price (MP), cost price (CP), and selling price (SP) of the article under different discount scenarios.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- A discount of 10% on the marked price results in a profit of 25%.
- We need to find the profit or loss percentage when a discount of 25% is applied to the marked price.

2. **Set Up the Equations:**
- Let the marked price (MP) be \( x \).
- The selling price (SP) after a 10% discount is:
\[ SP = MP - (10\% \text{ of } MP) = x - 0.1x = 0.9x \]
- The cost price (CP) can be calculated using the profit percentage:
\[ SP = CP + (25\% \text{ of } CP) = CP + 0.25 \times CP = 1.25 \times CP \]
- Setting the two expressions for SP equal gives:
\[ 0.9x = 1.25 \times CP \]

3. **Express CP in terms of MP:**
- Rearranging the equation gives:
\[ CP = \frac{0.9x}{1.25} = \frac{0.9x \times 100}{125} = \frac{90x}{125} = \frac{18x}{25} \]

4. **Calculate Selling Price with 25% Discount:**
- Now, if a discount of 25% is offered on the marked price:
\[ SP = MP - (25\% \text{ of } MP) = x - 0.25x = 0.75x \]

5. **Calculate Profit or Loss:**
- We now need to find the profit or loss when SP is \( 0.75x \) and CP is \( \frac{18x}{25} \).
- Profit or Loss = SP - CP:
\[ \text{Profit or Loss} = 0.75x - \frac{18x}{25} \]
- To combine these, convert \( 0.75x \) to a fraction:
\[ 0.75x = \frac{75x}{100} = \frac{15x}{20} = \frac{75x}{100} = \frac{75x}{100} = \frac{75x}{100} = \frac{75x}{100} = \frac{75x}{100} = \frac{75x}{100} = \frac{75x}{100} = \frac{75x}{100} = \frac{75x}{100} = \frac{75x}{100} = \frac{75x}{100} = \frac{75x}{100} = \frac{75x}{100} = \frac{75x}{100} \]
- Now, find a common denominator (which is 100):
\[ 0.75x = \frac{75x}{100}, \quad CP = \frac{72x}{100} \]
- Therefore:
\[ \text{Profit or Loss} = \frac{75x - 72x}{100} = \frac{3x}{100} \]

6. **Calculate Profit Percentage:**
- Profit Percentage = \(\frac{\text{Profit}}{\text{CP}} \times 100\):
\[ \text{Profit Percentage} = \frac{\frac{3x}{100}}{\frac{18x}{25}} \times 100 \]
- Simplifying gives:
\[ = \frac{3x}{100} \times \frac{25}{18x} \times 100 = \frac{3 \times 25}{18} = \frac{75}{18} \approx 4.1667 \text{ or } 4 \frac{1}{6} \% \]

### Final Answer:
The percentage profit when a discount of 25% is offered on the marked price is approximately \( 4 \frac{1}{6} \% \).