This question is based on the Avogadro's gas law, volume of gas proportional to no. of mol of gas.

Take note my method is based on when temperature does not change(because it says decomposed when heated)

Let X be the volume of O2 at the end
Therefore, 2/3 X of O3 decomposed at the start.

Total volume at the end = 20- 2/3 X + X
= 20+ 1/3 X
= 25

Thus X is 15cm^3

At the end you are left with 10cm^3 of O3 and 15cm^3 of O2

Edited: credit to Jerad

Think you've mixed up the decomposition. It should be ozone decomposing into oxygen, not the other way round.

There should be 15cm^3 of O2 and 10cm^3 of O3 left in the final reaction mixture instead of the other way round.