The cash difference between the selling price of an article at a profit of 2% and 14% is Rs. 4. The ratio of two selling prices is :
A. 17 : 19
B. 17 : 20
C. 19 : 20
D. 17 : 53

Options

A. C
B. D
C. B
D. A

Answer

To solve the problem, we need to find the ratio of the two selling prices (SP1 and SP2) given that the cash difference between them is Rs. 4. The selling prices correspond to profits of 2% and 14% on the cost price (CP).

### Step-by-Step Solution:

1. **Let the Cost Price (CP) be Rs. X.**
- We assume the cost price of the article is Rs. X.

2. **Calculate Selling Price at 2% Profit (SP1):**
- The selling price at a profit of 2% is given by:
\[ SP1 = CP + (2\% \text{ of } CP) = X + \frac{2}{100} \times X = X + 0.02X = 1.02X \]

3. **Calculate Selling Price at 14% Profit (SP2):**
- The selling price at a profit of 14% is given by:
\[ SP2 = CP + (14\% \text{ of } CP) = X + \frac{14}{100} \times X = X + 0.14X = 1.14X \]

4. **Find the Difference Between SP2 and SP1:**
- The difference between the two selling prices is:
\[ SP2 - SP1 = 1.14X - 1.02X = 0.12X \]
- According to the problem, this difference is Rs. 4:
\[ 0.12X = 4 \]

5. **Solve for X (Cost Price):**
- To find X, we divide both sides by 0.12:
\[ X = \frac{4}{0.12} = \frac{4 \times 100}{12} = \frac{400}{12} = \frac{100}{3} \approx 33.33 \text{ Rs.} \]

6. **Calculate SP1 and SP2:**
- Now we can find SP1 and SP2 using the value of X:
\[ SP1 = 1.02X = 1.02 \times \frac{100}{3} = \frac{102}{3} \text{ Rs.} \]
\[ SP2 = 1.14X = 1.14 \times \frac{100}{3} = \frac{114}{3} \text{ Rs.} \]

7. **Find the Ratio of SP1 to SP2:**
- The ratio of SP1 to SP2 is:
\[ \text{Ratio} = \frac{SP1}{SP2} = \frac{\frac{102}{3}}{\frac{114}{3}} = \frac{102}{114} \]
- Simplifying this fraction:
\[ \frac{102}{114} = \frac{51}{57} = \frac{17}{19} \]

### Final Answer:
The ratio of the two selling prices is **17:19**.