If 10% discount is allowed on the marked price of an article, the profit of a dealer is 20%. If he allows a discount of 20% his profit will be

Options

A. 4 `1/3` %
B. 0.05
C. 6 `2/3` %
D. 0.08

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step-by-Step Solution:

1. **Identify the Marked Price (MP)**:
Let's denote the marked price of the article as \( X \).

2. **Calculate Selling Price with 10% Discount**:
If a 10% discount is allowed on the marked price, the selling price (SP) can be calculated as:
\[ SP = X - \left( \frac{10}{100} \times X \right) = X - 0.1X = 0.9X \]

3. **Determine the Cost Price (CP) from Profit**:
We know that with this selling price, the dealer makes a profit of 20%. The profit percentage is given by:
\[ \text{Profit Percentage} = \frac{SP - CP}{CP} \times 100 \]
Substituting the known values:
\[ 20 = \frac{0.9X - CP}{CP} \times 100 \]
Rearranging gives:
\[ 0.2CP = 0.9X - CP \]
\[ 0.2CP + CP = 0.9X \]
\[ 1.2CP = 0.9X \]
\[ CP = \frac{0.9X}{1.2} = \frac{3X}{4} \]

4. **Calculate Selling Price with 20% Discount**:
Now, if a 20% discount is allowed, the new selling price can be calculated as:
\[ SP' = X - \left( \frac{20}{100} \times X \right) = X - 0.2X = 0.8X \]

5. **Determine New Profit Percentage**:
Now we need to find the new profit percentage with the new selling price:
\[ \text{New Profit Percentage} = \frac{SP' - CP}{CP} \times 100 \]
Substituting the values:
\[ \text{New Profit Percentage} = \frac{0.8X - \frac{3X}{4}}{\frac{3X}{4}} \times 100 \]
Simplifying the numerator:
\[ 0.8X - \frac{3X}{4} = \frac{4X}{5} - \frac{3X}{4} \]
Finding a common denominator (20):
\[ = \frac{16X}{20} - \frac{15X}{20} = \frac{X}{20} \]
Now substituting back:
\[ \text{New Profit Percentage} = \frac{\frac{X}{20}}{\frac{3X}{4}} \times 100 \]
Simplifying:
\[ = \frac{X}{20} \times \frac{4}{3X} \times 100 = \frac{4}{60} \times 100 = \frac{20}{3} \% \]

### Final Answer:
The new profit percentage when a 20% discount is allowed is \( \frac{20}{3} \% \).

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