Two objects of masses, $1\times {10}^{-3}\text{kg}$ and $4\times {10}^{-3}\text{kg}$ have equal momentum. What is the ratio of their kinetic energies?

The correct option is B $\text{4:1}$
We know that,
$KE=\frac{p^2}{2m}$

For a constant momentum,
$KE\propto \frac{1}{m}$
$\Rightarrow \frac{K{E}_1}{K{E}_2}=\frac{m_2}{m_1}$
$\Rightarrow \frac{K{E}_1}{K{E}_2}=\frac{4\times {10}^{-3}}{1\times {10}^{-3}}=\frac{4}{1}=4:1$