In an election between Sunita and Mamata, 85% of voters cast their votes but 2% of votes were invalid. If Sunita got 64,974 votes which is 78% of valid votes, then the total number of voters enrolled in the election was:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 1,00,000.
Let the total number of enrolled voters be x
Since 85% of voters cast their votes, the number of votes cast = 0.85 × x
Out of these votes, 2% were invalid, so 98% of the votes cast were valid.
The number of valid votes = 0.98 × (0.85 × x) = 0.833x
Sunita received 78% of the valid votes, which amounted to 64,974 votes
So,
⇒ 0.78 × (0.833 × x) = 64974
⇒ 0.64974 × x = 64974
⇒ x = 64974/0.64974
⇒ x = 100000
Thus, the total number of voters enrolled in the election is 100000