A shop keeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of cost price to the printed price of the book is

Let cost price = $$Rs.$$ $$100x$$ and marked price = $$Rs.$$ $$100y$$

To find : $$\frac{100x}{100y}=\frac{x}{y}=?$$

Now, profit % = 12%

=> $$S.P.=100x \times \frac{112}{100}=Rs.$$ $$112x$$ ------------(i)

Also, discount % = 10%

=> $$S.P.=100y \times \frac{90}{100}=Rs.$$ $$90y$$ ------------(ii)

From equations (i) and (ii), we get : 

=> $$112x=90y$$

=> $$\frac{x}{y}=\frac{90}{112}=\frac{45}{56}$$

$$\therefore$$ Ratio of cost price to the printed price of the book = 45 : 56

=> Ans - (A)