As,
$$
\begin{array}{ll}
\Rightarrow & K=\frac{1}{2 m} p^2 \\
\Rightarrow & p^2=2 m K \\
\Rightarrow & p=\sqrt{2 m K}
\end{array}
$$
Suppose, $p_1$ is the momentum of the body and $K_1=$ kinetic energy of the body initially. As the kinetic enery of the body is increased by $300 \%$, new kinetic energy of the body $=K_1+3 K_1$
Hence, percentage change in momentum
$$
\begin{aligned}
& =\frac{p_2-p_1}{p_1} \times 100 \\
& =\frac{\sqrt{2 m K_2}-\sqrt{2 m K_1}}{\sqrt{2 m K_1}} \times 100 \\
& =\frac{\sqrt{2 m} \sqrt{K_2}-\sqrt{K_1}}{\sqrt{2 m} \sqrt{K_1}} \times 100 \\
& =\frac{\sqrt{K_1+3 K_1}-\sqrt{K_1}}{\sqrt{K_1}} \times 100 \\
& =\frac{\sqrt{4 K_1}-\sqrt{K_1}}{\sqrt{K_1}} \times 100=100 \%
\end{aligned}
$$