Given data:
12% did not cast their vote
2% of the total cast votes were declared invalid
The winner received 46% of the total registered votes
Winner won by 1044 votes
Solution:
Let the total number of voters be V
⇒ Total votes cast = V × (88/100)
The valid votes = Total votes cast × (98/100)
⇒ The valid votes = V × (88/100) × (98/100)
Votes received by winning candidate = V × (46/100)
Votes received by losing candidate = Valid votes - Votes of winner
⇒ [V × (88/100) × (98/100)] - [V × (46/100)]
According to the question
The winner defeated his opponent by 1044 votes
⇒ 10046V - (100×10088×98×V - 10046V) = 1044
⇒ 10046V - 100008624V + 10046V = 1044
⇒ 10092V - 100008624V = 1044
⇒ 100009200V - 100008624V = 1044
⇒ 10000576V = 1044
⇒ V = 18125
∴ The total number of voters registered in the election was 18125.
Shortcut Trick
Let total votes = 10000
So,
vote cast = 88% of 10000 = 8800
Invalid votes = 2% of 8800 = 176
So,
valid votes = 8800 - 176 = 8624
Winner got = 46% of total votes = 46% of 10000 = 4600
So, loser got = 8624 - 4600 = 4024
So, difference between winner and loser = 4600 - 4024 = 576
Here,
576 = 1044 votes
So,
Total registered votes = (1044/576) × 10000 = 18125