Answer :
The number of valid votes is 2400
How to find the total number
In the election, 10% of the total voters did not vote. Therefore, the number of voters who cast their votes is 90% of the total voters. Let the total number of voters be x. Then, the number of valid votes is:
0.9x - 300
Let the number of valid votes for the winner be y. Then, the number of valid votes for the loser is:
0.9x - 300 - y
We know that the winner gets 60% of the total voters and wins by 900 votes. Therefore, we have:
y - (0.9x - 300 - y) = 900
Simplifying the expression, we get:
2y - 0.9x + 300 = 900
2y - 0.9x = 600
We also know that the total number of valid votes is equal to the difference between the total number of voters and the number of invalid votes. Therefore, we have:
0.9x - 300 + 300 = x - 300
Simplifying the expression, we get:
0.9x = x - 300
0.1x = 300
x = 3000
Substituting x = 3000 into the equation 2y - 0.9x = 600, we get:
2y - 0.9(3000) = 600
2y - 2700 = 600
2y = 3300
y = 1650
Therefore, the number of valid votes is:
0.9x - 300 = 0.9(3000) - 300 = 2400
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