The price of a book was P before any changes.
We know that the book got two successive increases of $$x \%$$ each, so the net percentage change in the price of the book was $$\left(x+x+\frac{x \times x}{100}\right) \%=\left(2 x+x^2 \%\right) \%$$
(When there are two successive changes i.e. $$a \%$$ & $b\%$the net percentage change in their product is of $$\left(a+b+\frac{a b}{100}\right) \%$$ )

So, the final price of the book after two successive increases of $$x \%$$ each will be $$\mathrm{P}+\left(2 \mathrm{x}+\mathrm{x}^2 \%\right) \% \times \mathrm{P}=\mathrm{P}\left(1+\left(2 \mathrm{x}+\mathrm{x}^2 \%\right) \%\right)=\mathrm{P}(1+\mathrm{x} \%)^2$$

Hence options (B) \& (D) are correct.