A shopkeeper earns a profit of `17%` on selling a book at `10%` discount on the printed price. The ratio of the C.P to the printed price of the book is

Options

A. `9:17`
B. `10:13`
C. `13:17`
D. `10:17`

Answer

To solve the problem step-by-step, we need to establish the relationship between the cost price (C.P.), printed price (P.P.), profit percentage, and discount percentage.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Profit Percentage = 17%
- Discount Percentage = 10%

2. **Define the Variables:**
- Let the Cost Price (C.P.) be \( C \).
- Let the Printed Price (P.P.) be \( P \).

3. **Establish the Relationship:**
- When a book is sold at a discount, the selling price (S.P.) can be expressed as:
\[ S.P. = P - (10\% \text{ of } P) = P \times (1 - 0.10) = 0.90P \]
- The profit is given as 17%, which means:
\[ S.P. = C + (17\% \text{ of } C) = C \times (1 + 0.17) = 1.17C \]

4. **Set Up the Equation:**
- Since both expressions represent the selling price (S.P.), we can set them equal to each other:
\[ 0.90P = 1.17C \]

5. **Rearranging the Equation:**
- To find the ratio of C.P. to P.P., we rearrange the equation:
\[ \frac{C}{P} = \frac{0.90}{1.17} \]

6. **Calculate the Ratio:**
- Simplifying the fraction:
\[ \frac{C}{P} = \frac{0.90 \times 100}{1.17 \times 100} = \frac{90}{117} \]
- Now, we can simplify \( \frac{90}{117} \):
- The GCD of 90 and 117 is 9.
- Dividing both the numerator and denominator by 9:
\[ \frac{90 \div 9}{117 \div 9} = \frac{10}{13} \]

7. **Final Ratio:**
- Therefore, the ratio of the Cost Price to the Printed Price is:
\[ \frac{C}{P} = \frac{10}{13} \]

### Conclusion:
The ratio of the Cost Price to the Printed Price of the book is \( 10:13 \).