Mohan earns a profit of 20% selling a jean at 15% discount on printed price. The ratio of the cost price to printed price of the jean is
A 17:24
B. 17:34
C. 16:13
D. 21:23

Options

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

Answer

To solve the problem, we need to find the ratio of the cost price (CP) to the printed price (PP) of the jean given the profit percentage and discount percentage.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Profit Percentage (P) = 20%
- Discount Percentage (D) = 15%

2. **Understand the Relationship:**
- The printed price (PP) is also known as the marked price.
- The selling price (SP) can be calculated using the formula:
\[ SP = PP - (D \times PP / 100) = PP \times (1 - D/100) \]
- The cost price (CP) can be calculated using the formula:
\[ CP = SP / (1 + P/100) \]

3. **Calculate Selling Price (SP) in terms of Printed Price (PP):**
\[ SP = PP \times (1 - 0.15) = PP \times 0.85 \]

4. **Substitute SP into the CP formula:**
\[ CP = \frac{SP}{1 + P/100} = \frac{PP \times 0.85}{1 + 0.20} = \frac{PP \times 0.85}{1.20} \]

5. **Simplify the Expression:**
\[ CP = \frac{PP \times 0.85}{1.20} = PP \times \frac{0.85}{1.20} \]
- Now, calculate \(\frac{0.85}{1.20}\):
\[ \frac{0.85}{1.20} = \frac{85}{120} = \frac{17}{24} \]

6. **Determine the Ratio of Cost Price to Printed Price:**
\[ \frac{CP}{PP} = \frac{17}{24} \]

7. **Final Answer:**
The ratio of the cost price to the printed price of the jean is \( \frac{17}{24} \).

### Conclusion:
The correct option is **A. 17:24**.