The kinetic energy of a body is directly proportional to the square of its velocity. If velocity increases by 50% then the percentage increase in its kinetic energy is 

We know, Kinetic Energy, $\mathrm{K}=\frac{1}{2}{\mathrm{mv}}^2$

${\mathrm{K}}_1=\frac{1}{2}{{\mathrm{mv}}_1}^2$ and ${\mathrm{K}}_2=\frac{1}{2}{{\mathrm{mv}}_2}^2$ 

As Kinetic energy is proportional to v², we get

$\frac{{\mathrm{K}}_2}{{\mathrm{K}}_1}={\left(\frac{{\mathrm{v}}_2}{{\mathrm{v}}_1}\right)}^2$

If the initial velocity is 100 then the final velocity is 150, 

$\% \mathrm{change} \mathrm{in} \mathrm{Kinetic} \mathrm{energy}=\frac{{\mathrm{K}}_2-{\mathrm{K}}_1}{{\mathrm{K}}_1}\times 100$

$\mathrm{Or}, \left(\frac{{\mathrm{K}}_2}{{\mathrm{K}}_1}-1\right)\times 100=\left(\frac{{\mathrm{v}}_2^2}{{\mathrm{v}}_1^2}-1\right)\times 100$

$\mathrm{or} \% \mathrm{change} \mathrm{in} \mathrm{Kinetic} \mathrm{energy}=\left(\frac{225}{100}-1\right)\times 100=125\%$.

Hence, kinetic energy is increased by 125%.