Question

Two objects of masses 1kg and 3kg have equal momentum what is the ratio of kinetic energy

Answer 1

The ratio of the kinetic energies = 3:1 

The momentum of the two masses are equal; so, the velocities are in the ration 3:1 
The ratio of the kinetic energies are also 3:1 

Let the v=6m/s for 1kg mass and 
v= 2m/s for the 3 kg mass so, they have equal momentum [1x6 = 2x3] 

ratio of KEs ½ mv² 
= ½ x1 x 6² : ½ x 3 x 4² 
= 18 : 6 
= 3:1 

Answer 2

As we know
Momentum = mv
1v = 3V

Kinetic Energy = 1/2 m v²
therefore for 1kg mass
K1 = 1/2 x 1x v² = 1/2 x (3V)² = 9/2 V²

and for 3kg mass 
K3= 1/2 x 3 x V²

Ratio
(K1/K3) = 9/3 = 3