Hey,

Let i1 be the initial rotation and w1 the initial angular speed.

We know that angular momentum is L=I1w1

Initial kinetic energy k1=Lw1/2

after collapsing the rotational inertia decreases by 1/3, therefore new inertia will be i2=i1/3

let w2 be new angular speed.

Since the net torque is zero the angular momentum does not change after collapse that is

i1w1=i1*w2/3

w2=3w1

thus, new rotational kinetic energy after collapse is:

k2=Lw2/2=3Lw1/2

Therefore the new rotational kinetic energy to initial kinetic enrgy will be

k1/k2=(3Lw1/2)*(2/lw1)=3

Thus 3 is the required answer.

I hope this helps.

All the best!