In a bungee jump where the total energy at the top is 60,000 J and air resistance is ignored, which energy store of the rope increases as it stretches?

What the question is asking

A bungee rope acts like a spring. When it is pulled longer than its natural length, energy is stored in the rope itself.

Energy transfer during the jump (no air resistance)

With air resistance ignored, mechanical energy is conserved. As the jumper falls, energy is transferred from the gravitational potential energy store into other stores.

Which store in the rope increases?

The rope stretches and deforms, so energy builds up in the rope’s elastic potential energy store. The more it stretches, the more elastic potential energy it stores (similar to a stretched spring, often modeled by $E = \tfrac{1}{2}kx^2$).