A shopkeeper carns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is

CP = Cost Price of the book MP = Marked (Printed) Price of the book SP = Selling Price of the book D = Discount Percentage P = Profit Percentage

We are given:

1. Profit Percentage (P) = 12%
2. Discount Percentage (D) = 10%

We need to find the ratio of CP to MP.

We know that:

Profit Percentage (P) = [(SP - CP) / CP] * 100 Discount Percentage (D) = [(MP - SP) / MP] * 100

Let's use these formulas to find CP/MP:

1. Profit Percentage (P) = 12% = 12/100 = 0.12
2. Discount Percentage (D) = 10% = 10/100 = 0.10

Using the profit formula:

0.12 = [(SP - CP) / CP]

Now, let's use the discount formula:

0.10 = [(MP - SP) / MP]

We can rearrange the first equation to find SP in terms of CP:

SP = CP + 0.12 * CP SP = 1.12 * CP

Similarly, we can rearrange the second equation to find SP in terms of MP:

SP = MP - 0.10 * MP SP = 0.90 * MP

Now, we can set these two expressions for SP equal to each other since they both represent the selling price:

1.12 * CP = 0.90 * MP

Now, let's find the ratio of CP to MP:

CP/MP = 0.90 / 1.12

To simplify this ratio, we can multiply both the numerator and denominator by 100 to get rid of the decimals:

CP/MP = (0.90 * 100) / (1.12 * 100) CP/MP = 90/112

Now, we can simplify this ratio by dividing both the numerator and denominator by their greatest common divisor, which is 2:

CP/MP = (90/2) / (112/2) CP/MP = 45/56

So, the ratio of the cost price (CP) to the marked price (MP) of the book is 45:56. The correct answer is 45:56.