In an election between two candidates, 8% of the votes were invalid. The winning candidate got 60% of the total valid votes and won the election by 5888 votes. How many voters were registered?

Let the total number of registered voters be x.
Since 8% of the votes were invalid, the number of valid votes is:

Valid votes=(100%−8%) of x=92% of x=0.92x
The winning candidate got 60% of the total valid votes.
Therefore, the losing candidate must have received the remaining valid votes:

Losing candidate’s share=100%−60%=40% of the valid votes
The difference in votes between the winner and the loser is:

Difference=60%−40%=20% of the valid votes
We are given that the winning candidate won by 5888 votes. Thus:

20% of (0.92x)=5888
Converting percentages into fractions/decimals:

100
20
​
×
100
92
​
×x=5888
5
1
​
×
100
92
​
×x=5888
500
92
​
×x=5888
x=
92
5888×500
​

Dividing 5888 by 92:

92
5888
​
=64
x=64×500=32000
Hence, the total number of registered voters was 32000.