In an election there are a total of 4,000 registered voters out of which x% of voters did not cast their votes and 180 votes are declared invalid. The winner got 740 votes more than the losing candidate. The number of valid votes received by the winner are 42% of the total registered voters. How many registered voters did not cast their vote?

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.