When an 81.0-kg adult uses a spiral staircase to climb to the second floor of his house, his gravitational potential energy increases by 2.25 103 j. by how much does the potential energy of a(n) 17.5-kg child increase when the child climbs a normal staircase to the second floor?

Assuming both staircases are of equal height from the ground floor, then the nature of the staircase does not change the gravitational potential energy.

We can, from information given, find the height of the floor, and then apply to the child using the standard formula, E=mgh.

However, in this case, it is a matter of proportions, i.e.

81.0 kg : 2.25 kJ

17.5 kg : x kJ

cross multiply to get

x=2.25*17.5/81=0.486 kJ (or 486 J) to three significant figures.