In an election there are a total of 4,000 registered

Solution

Let the total number of registered voters = T = 4000 Number of voters who did not casted their votes = x% of Registered voters So, number of voters who casted their votes = (100 – x)% of Registered voters Out of casted votes, 180 were declared invalid. So, number of valid votes = (100 – x)% of T – 180 Number of votes, winning candidate gets = 42% of T The number of votes received by losing candidate = (100 – x)% of T – 180 – 42% of T     = (58 – x)% of T – 180 Difference of votes between winner and loser = 42% of T – [(58 – x)% of T – 180] = 740 (x – 16)% of T + 180 = 740 (x – 16)% of 4000 = 560 x – 16 = 14 x = 30 Registered voters who did not casted their votes = x% of 4000 = 30% of 4000 = 1200 Hence, option a) is the correct answer.