Explanation:

- The shopkeeper sells a book with a 10% discount on its printed price.

- Despite the discount, they manage to earn a 12% profit.

- To find the cost price to the printed price ratio, consider both the discount and profit margins.

Let's break it down:

1. Suppose the printed price is 100 units.

2. After a 10% discount, the selling price becomes 90 units.

3. The profit margin is 12%, so the cost price x (1 + 12/100) = selling price.

4. Hence, 1.12x = 90.

5. Solving for x: x = 90/1.12 = 80.36 approximately.

6. The cost price is about 80.36 units when the printed price is 100 units.

7. Convert this into the simplest ratio of cost price to printed price:

- 80.36 : 100 simplifies to 45 : 56.

- Therefore, the correct answer is Option: 2, 45 : 56.