Question

In an election, 10% of the voters on the voter's list did not case their votes and 60 voters cast their ballet papers blank. There were only two candidates, the winner was supported by 47% of all voters in the list and he got 308 votes more than his rival. Find the total number of voters on the list.

Answer 1

Suppose there were N members in the voter list.
Suppose W votes were in favour of the winner.
Suppose L votes were in favour of the loser.
So $90\%$ of N or 0.90N cast votes
60 votes were declared invalid
So 0.90N - 60votes were valid.
Winning candidate secured 308 votes more than losing candidate.
W = L + 308
W + L = 0.90N - 60
If $47\%$ of the total member voted in favour of winning candidate.
W = .47N
We have 3 equations
W = L + 308
W + L = 0.90N - 60
W = .47N
Substitute 47N in the first two:
.47N = L + 308
.47N + L = 0.90N - 60
Multiply each through by 100
47N = 100L + 30800
47N + 100L = 90N-6000
47N - 100L = 30800
-43N + 100L = -6000
$\underset{–}{}$
4N = 24800
N = 6200.