Given,

Mass of body A = 5 kg

Mass of body B = 8 kg

Momentum of body B is twice that of body A,

$$\therefore$$ $${P_B} = 2{P_A}$$

We know,

Kinetic Energy $$(K) = {{{P^2}} \over {2m}}$$

$$\therefore$$ $${{{K_A}} \over {{K_B}}} = {\left( {{{{P_A}} \over {{P_B}}}} \right)^2} \times {{{m_B}} \over {{m_A}}}$$

$$ = {\left( {{1 \over 2}} \right)^2} \times {8 \over 5}$$

$$ = {1 \over 4} \times {8 \over 5}$$

$$ = {2 \over 5}$$