In an election between two candidates, 75% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 9504 votes, which were 80% of the valid votes. Find the total number of votes enrolled in that election.
- A12,672
- B13,200
- C16,500
- D12,375
Solution & Step-by-step Explanation
Let the total number of enrolled voters be x.
Number of votes cast = 75% of x=
100
75
x=
4
3
x
Out of these votes, 4% were invalid, meaning 96% were valid:
Valid votes=96% of (
4
3
x)=
100
96
×
4
3
x=
25
24
×
4
3
x=
25
18
x
The winning candidate got 80% of the valid votes, which equals 9504:
80% of (
25
18
x)=9504
5
4
×
25
18
x=9504
125
72
x=9504
x=
72
9504×125
x=132×125=16,500
The total number of enrolled votes is 16,500.
Number of votes cast = 75% of x=
100
75
x=
4
3
x
Out of these votes, 4% were invalid, meaning 96% were valid:
Valid votes=96% of (
4
3
x)=
100
96
×
4
3
x=
25
24
×
4
3
x=
25
18
x
The winning candidate got 80% of the valid votes, which equals 9504:
80% of (
25
18
x)=9504
5
4
×
25
18
x=9504
125
72
x=9504
x=
72
9504×125
x=132×125=16,500
The total number of enrolled votes is 16,500.