In an election between 2 candidates, 5% of the votes were invalid. The winning candidate got 2200 votes and the losing candidate got 1600 votes. The losing candidate got what percentage of the total votes cast?

Let's assume the total number of the vote cast in the election is 100y.

In an election between 2 candidates, 5% of the votes were invalid.

Valid votes = 100y of (100-5)%

= 100y of 95%

= $$100y\times\frac{95}{100}$$

= 95y

The winning candidate got 2200 votes and the losing candidate got 1600 votes.

95y = 2200+1600

95y = 3800

y = 40

total number of the vote cast in the election = 100y

= $$100\times40$$

= 4000

Percentage of votes the losing candidate got out of the total votes cast = $$\frac{1600}{4000}\times100$$

= $$\frac{160}{4}$$

= 40%