The cash difference between the selling price of an article at a profit of 4% and 8% is Rs. 3. The ratio of two selling prices is:

Options

A. `25:27`
B. `26:27`
C. `26:31`
D. `26:29`

Answer

To solve the problem, we need to find the ratio of the two selling prices of an article sold at a profit of 4% and 8%, given that the cash difference between these two selling prices is Rs. 3.

### Step-by-Step Solution:

1. **Define the Cost Price (CP)**:
Let the cost price of the article be \( CP \).

2. **Calculate Selling Price at 4% Profit**:
The selling price (SP) when sold at a profit of 4% can be calculated as:
\[ SP_1 = CP + 0.04 \times CP = 1.04 \times CP \]

3. **Calculate Selling Price at 8% Profit**:
The selling price when sold at a profit of 8% can be calculated as:
\[ SP_2 = CP + 0.08 \times CP = 1.08 \times CP \]

4. **Set Up the Equation for the Difference**:
According to the problem, the difference between the two selling prices is Rs. 3:
\[ SP_2 - SP_1 = 3 \]
Substituting the expressions for \( SP_1 \) and \( SP_2 \):
\[ (1.08 \times CP) - (1.04 \times CP) = 3 \]

5. **Simplify the Equation**:
Simplifying the left side:
\[ 1.08 \times CP - 1.04 \times CP = 0.04 \times CP = 3 \]

6. **Solve for Cost Price (CP)**:
To find \( CP \), divide both sides by 0.04:
\[ CP = \frac{3}{0.04} = 75 \]

7. **Calculate Selling Prices**:
Now that we have \( CP = 75 \):
- Selling Price at 4% profit:
\[ SP_1 = 1.04 \times 75 = 78 \]
- Selling Price at 8% profit:
\[ SP_2 = 1.08 \times 75 = 81 \]

8. **Find the Ratio of Selling Prices**:
The ratio of the two selling prices is:
\[ \text{Ratio} = \frac{SP_1}{SP_2} = \frac{78}{81} \]
Simplifying this ratio:
\[ \text{Ratio} = \frac{78 \div 3}{81 \div 3} = \frac{26}{27} \]

### Final Answer:
The ratio of the two selling prices is \( \frac{26}{27} \).