If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be:

Kinetic energy and momentum are related by $$KE = \frac{p^2}{2m}$$, so $$p = \sqrt{2m \cdot KE}$$, meaning $$p \propto \sqrt{KE}$$.

If the kinetic energy becomes 4 times its initial value, i.e., $$KE_f = 4\,KE_i$$, then $$p_f = \sqrt{4\,KE_i \cdot 2m} = 2\sqrt{2m \cdot KE_i} = 2p_i$$.

The percentage change in momentum is $$\frac{p_f - p_i}{p_i} \times 100 = \frac{2p_i - p_i}{p_i} \times 100 = 100\%$$.