(a)

The total percentage of those who voted is 100%

The percentage obtained by those who lost = 100% - 87.5%

The percentage obtained by those who lost = 12.5%

Votes obtained by the candidates who lost = 275

If 12.5% = 275

87.5% = $\frac{\mathrm{275\; x\; 87.5\%}}{\mathrm{12.5\%}}$ = 1925

∴ The winner obtained 1925 votes

(b)

Total number of voters = Winner Votes + Losers Votes

Total number of voters = 1925 + 275

Total number of voters = 2200

The percentage of eligible voters is 100%

Percentage that turned out is 55% and the total was 2200

If 55% = 2200

100% = $\frac{\mathrm{2200\; x\; 100\%}}{\mathrm{55\%}}$ = 4000

∴ number of eligible voters = 4000