A shopkeeper earns 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:

A shopkeeper earns 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: Correct Answer 45 : 56

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{CP}}\,{\text{be}}\,100 \cr & {\text{Hence}}, \cr & {\text{SP}} = 100 + 12\% \,of\,100 \cr & \,\,\,\,\,\,\, = 112 \cr & {\text{If}}\,{\text{the}}\,{\text{marked}}\,{\text{price}}\,{\text{be}}\,X,\,{\text{then}} \cr & 90\% \,of\,X = 112 \cr & \Rightarrow x = \frac{{ {112 \times 100} }}{{90}} \cr & \Rightarrow x = Rs.\,\frac{{1120}}{9} \cr & {\text{Hence}}, \cr & {\text{Required}}\,{\text{ratio}} \cr & = 100:\,\frac{{1120}}{9} \cr & = 900:1120 \cr & = 45:56 \cr} $$