In a village, only 63% of the registered voters could cast their votes and none of the votes cast were invalid. Only two candidates were contesting the election and the respective ratio of the votes received by them is 4 : 5. If the winning candidate received 1120 votes, what is the number of registered voters in the village ?

Let the number of registered voters in the village = $$100x$$

=> No. of voters who cast their votes = $$\frac{63}{100} \times 100x = 63x$$

Let no. of votes received by winning candidate = $$5y$$

=> No. of votes received by losing candidate = $$4y$$

Acc to ques,

=> $$5y = 1120$$

=> $$y = \frac{1120}{5} = 224$$

=> Total votes = $$5y + 4y = 9y$$

= $$9 \times 224 = 2016$$

Now, total casted votes = $$63x = 2016$$

=> $$x = \frac{2016}{63} = 32$$

$$\therefore$$ Number of registered voters = 32 * 100 = 3200