A dealer allows 25% discount on the marked price of articles and carns a profit of 20% on them. What is the marked price of the article on which he gains Rs 800?

Options

A. Rs6000
B. Rs6400
C. Rs7200
D. Rs7000

Answer

To solve the problem step by step, we will follow the logic used in the video transcript.

### Step-by-Step Solution:

1. **Define Variables**:
Let the marked price of the article be \( X \).

2. **Calculate the Discount**:
The dealer allows a discount of 25% on the marked price. Therefore, the discount amount can be calculated as:
\[ \text{Discount} = 25\% \text{ of } X = \frac{25}{100} \times X = \frac{X}{4} \]

3. **Calculate the Selling Price**:
The selling price (SP) after applying the discount is:
\[ \text{Selling Price} = \text{Marked Price} - \text{Discount} = X - \frac{X}{4} = \frac{4X}{4} - \frac{X}{4} = \frac{3X}{4} \]

4. **Profit Calculation**:
We know that the dealer earns a profit of 20%. Profit is defined as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} \]
Given that the profit is Rs. 800, we can express this as:
\[ \text{Selling Price} - \text{Cost Price} = 800 \]

5. **Cost Price Calculation**:
The profit percentage formula is:
\[ \text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100 \]
Substituting the known values:
\[ 20 = \frac{800}{\text{Cost Price}} \times 100 \]
Rearranging gives:
\[ \text{Cost Price} = \frac{800 \times 100}{20} = 4000 \]

6. **Relate Selling Price to Cost Price**:
From the profit equation:
\[ \text{Selling Price} - 4000 = 800 \]
Therefore, the selling price is:
\[ \text{Selling Price} = 4000 + 800 = 4800 \]

7. **Set Selling Price Equal to Expression**:
We have already established that:
\[ \text{Selling Price} = \frac{3X}{4} \]
Setting this equal to the selling price we calculated:
\[ \frac{3X}{4} = 4800 \]

8. **Solve for Marked Price**:
To find \( X \), multiply both sides by 4:
\[ 3X = 4800 \times 4 \]
\[ 3X = 19200 \]
Now, divide by 3:
\[ X = \frac{19200}{3} = 6400 \]

9. **Conclusion**:
Therefore, the marked price of the article is:
\[ \text{Marked Price} = Rs. 6400 \]