The MP of an article is `30%` higher than its CP and `20%` discount is allowed on this article, then the profit percentage

Options

A. `10%`
B. `14%`
C. `4%`
D. `26%`

Answer

To solve the problem step by step, we will follow the information given in the question regarding the cost price (CP), market price (MP), discount, and profit percentage.

### Step-by-Step Solution:

1. **Assume the Cost Price (CP):**
Let's assume the Cost Price (CP) of the article is ₹100.
- **Hint:** Start with a simple assumption to make calculations easier.

2. **Calculate the Market Price (MP):**
The Market Price (MP) is 30% higher than the CP.
\[ MP = CP + 30\% \text{ of } CP = 100 + 0.30 \times 100 = 100 + 30 = ₹130 \]
- **Hint:** To find a percentage increase, multiply the original amount by the percentage (as a decimal) and add it to the original amount.

3. **Calculate the Selling Price (SP) after Discount:**
A discount of 20% is allowed on the Market Price.
\[ \text{Discount} = 20\% \text{ of } MP = 0.20 \times 130 = ₹26 \]
Therefore, the Selling Price (SP) after the discount is:
\[ SP = MP - \text{Discount} = 130 - 26 = ₹104 \]
- **Hint:** To find the selling price after a discount, subtract the discount amount from the market price.

4. **Calculate the Profit:**
Profit is calculated as the difference between the Selling Price (SP) and the Cost Price (CP).
\[ \text{Profit} = SP - CP = 104 - 100 = ₹4 \]
- **Hint:** Profit is simply the selling price minus the cost price.

5. **Calculate the Profit Percentage:**
The profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{CP}} \right) \times 100 \]
Substituting the values:
\[ \text{Profit Percentage} = \left( \frac{4}{100} \right) \times 100 = 4\% \]
- **Hint:** To find the profit percentage, divide the profit by the cost price and multiply by 100.

### Final Answer:
The profit percentage is **4%**.