The cash difference between the selling price of an article at a profit of 2% and 18% is Rs3. The ratiio of two selling prices is.

Options

A. `51:59`
B. `51:53`
C. `51:60`
D. `55:59`

Answer

To solve the problem, we need to find the ratio of the selling prices of an article sold at a profit of 2% and 18%, given that the cash difference between these two selling prices is Rs 3.

### Step-by-Step Solution:

1. **Let the Cost Price (CP) of the article be Rs X.**

2. **Calculate the Selling Price (SP) at 2% Profit:**
- The formula for selling price at a profit is:
\[ SP = CP + (Profit \% \times CP) \]
- For 2% profit:
\[ SP_{2\%} = X + \left(\frac{2}{100} \times X\right) = X + \frac{2X}{100} = \frac{102X}{100} \]

3. **Calculate the Selling Price (SP) at 18% Profit:**
- For 18% profit:
\[ SP_{18\%} = X + \left(\frac{18}{100} \times X\right) = X + \frac{18X}{100} = \frac{118X}{100} \]

4. **Find the Difference between the Two Selling Prices:**
- According to the problem, the difference between the two selling prices is Rs 3:
\[ SP_{18\%} - SP_{2\%} = 3 \]
- Substituting the selling prices we calculated:
\[ \frac{118X}{100} - \frac{102X}{100} = 3 \]
- Simplifying this:
\[ \frac{118X - 102X}{100} = 3 \]
\[ \frac{16X}{100} = 3 \]
\[ 16X = 300 \]
\[ X = \frac{300}{16} = 18.75 \]

5. **Calculate the Selling Prices:**
- Now we can find the actual selling prices using the cost price:
\[ SP_{2\%} = \frac{102 \times 18.75}{100} = 19.125 \]
\[ SP_{18\%} = \frac{118 \times 18.75}{100} = 22.125 \]

6. **Find the Ratio of the Two Selling Prices:**
- The ratio of the two selling prices is:
\[ \text{Ratio} = SP_{2\%} : SP_{18\%} = \frac{102X}{100} : \frac{118X}{100} \]
- This simplifies to:
\[ 102 : 118 \]
- To simplify further, divide both numbers by 2:
\[ 51 : 59 \]

### Final Answer:
The ratio of the two selling prices is **51 : 59**.