Given,

Mass of electrons, $m_e=9.11\times {10}^{-31}kg$

Mass of proton, $m_p=1.67\times {10}^{-27}kg$

The kinetic energy of the electron is,

$E_e=10keV={10}^{4}eV$

$E_e={10}^4\times 1.6\times {10}^{-19}=1.60\times {10}^{-15}J$

The kinetic energy of the proton is,

$E_p=100keV={10}^{5}eV=1.60\times {10}^{-14}J$

The relationship between an electron's kinetic energy and velocity, $v_e$, is as follows:

$E_e=\frac{1}{2}m{v_e}^2$

$v_e=\frac{2\times 1.6\times {10}^{-15}}{9.11\times {10}^{-31}}=5.93\times {10}^{7}m/s$

The relationship between a proton's kinetic energy and velocity, $v_p$, is as follows:

$E_p=\frac{1}{2}m{v_p}^2$

$v_p=4.38\times {10}^{6}m/s$

Electrons move more quickly than protons because their velocities are greater.

Thus the ratio,

$\frac{v_e}{v_p}=\frac{5.93\times {10}^7}{4.38\times {10}^6}=\frac{13.53}{1}$

Hence the correct answer is 13.53.