A book seller allowing a $12\%$ discount on the marked price of a book made a profit of $10\%$. What will be his percentage of profit if he sells the book at the marked price?

Let the Marked Price ($\text{MP}$) be $100$.
A discount of $12\%$ is given on the $\text{MP}$:

$$\text{Selling Price (SP)}=100-12=88$$

At this $\text{SP}$, the book seller makes a profit of $10\%$. Therefore:

$$\text{Cost Price (CP)}=\frac{\text{SP}}{1+\frac{\text{Profit Percentage}}{100}}$$

$$\text{CP}=\frac{88}{1+\frac{10}{100}}=\frac{88}{1.1}=80$$

If he sells the book at the marked price, the new selling price $({\text{SP}}_{\text{new}})$ becomes equal to the $\text{MP}$:

$${\text{SP}}_{\text{new}}=100$$

The new profit percentage is:

$$\text{New Profit Percentage}=\left(\frac{{\text{SP}}_{\text{new}}-\text{CP}}{\text{CP}}\right)\times 100$$

$$\text{New Profit Percentage}=\left(\frac{100-80}{80}\right)\times 100=\frac{20}{80}\times 100=25\%$$