For a certain article, if discount is 25% the profit is 25%. If the discount is 10%, then the profit is

Options

A. `50%`
B. `40%`
C. `30%`
D. `33(1)/(3)%`

Answer

To solve the problem step by step, we will first establish the relationship between cost price (CP), market price (MP), discount, and profit.

### Step 1: Establish the relationship between CP and MP
Given:
- When the discount is 25%, the profit is 25%.

Let’s assume the cost price (CP) of the article is 100.

- If the profit is 25%, then the market price (MP) can be calculated as:
\[ MP = CP + \text{Profit} = 100 + 25 = 125 \]

### Step 2: Calculate the selling price (SP) with a 25% discount
- A 25% discount on the market price (MP) of 125 means:
\[ \text{Discount} = 25\% \text{ of } 125 = \frac{25}{100} \times 125 = 31.25 \]
- Therefore, the selling price (SP) after the discount is:
\[ SP = MP - \text{Discount} = 125 - 31.25 = 93.75 \]

### Step 3: Verify the profit with the selling price
- The profit can be calculated as:
\[ \text{Profit} = SP - CP = 93.75 - 100 = -6.25 \]
This indicates that our initial assumption of CP being 100 is incorrect. We need to adjust our calculations based on the ratios derived from the profit and discount.

### Step 4: Establish the ratio of CP to MP
From the information given:
- The ratio of CP to MP when the profit is 25% and discount is 25% can be established as:
\[ \frac{CP}{MP} = \frac{100 - \text{Discount}}{100 + \text{Profit}} = \frac{100 - 25}{100 + 25} = \frac{75}{125} = \frac{3}{5} \]

### Step 5: Calculate CP and MP
Let’s denote CP as 3x and MP as 5x. This means:
- \( CP = 3x \)
- \( MP = 5x \)

### Step 6: Calculate SP with a 10% discount
Now, if the discount is 10%, we can calculate the new selling price:
- A 10% discount on MP (5x) means:
\[ \text{Discount} = 10\% \text{ of } 5x = 0.1 \times 5x = 0.5x \]
- Therefore, the new selling price (SP) is:
\[ SP = MP - \text{Discount} = 5x - 0.5x = 4.5x \]

### Step 7: Calculate the profit with the new SP
- The profit can now be calculated as:
\[ \text{Profit} = SP - CP = 4.5x - 3x = 1.5x \]

### Step 8: Calculate the profit percentage
- The profit percentage can be calculated as:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{CP} \right) \times 100 = \left( \frac{1.5x}{3x} \right) \times 100 = 50\% \]

### Conclusion
Thus, when the discount is 10%, the profit percentage is **50%**.

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