Take S to the the set of all voters eligible to vote in the last two elections. The events we are interested in are

E: a voter voted in the first; P(E) = 0.25
F: a voter voted in the second; P(F) = x (this is the unknown)
EF: a voter voted in both; P(EF) = 0.20
EF: a voter voted in at least one election; P(EF) = 10.35 = 0.65
(since 35% voted in neither, the remaining 65% voted in at least one election).

Putting all this together,

P(EF) = P(E) + P(F)P(EF)

0.65 = 0.25 + x 0.20,

giving x = 0.60, or 60%