In an election between two candidates, 75% of the voters cast their votes, out of which 2% of the votes were declared invalid. A candidate got 9,261 votes, which were 75% of the total valid votes. Find the total number of votes.

Let the total number of votes be x.
Number of votes cast = 75% of x=
100
75
​
x

Since 2% of the votes were invalid, 98% of the cast votes were valid:

Valid votes=
100
98
​
×
100
75
​
x
The candidate got 75% of the total valid votes, which equals 9,261:

100
75
​
×(
100
98
​
×
100
75
​
x)=9261
4
3
​
×
50
49
​
×
4
3
​
x=9261
800
441
​
x=9261
Solving for x:

x=
441
9261×800
​

Notice that 441=21
2
and 9261=21
3
, so
441
9261
​
=21.

x=21×800=16,800
Thus, the total number of votes is 16,800.