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In a village only 63% of the registered ...

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 elections and the ratio of the votes received by them was 4:5. If the winning candidate received 1120 votes, what is the number of registered voters in the village?

A

3200

B

3400

C

3600

D

3160

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we can follow these steps: ### Step 1: Define the total number of registered voters Let the total number of registered voters in the village be \( x \). ### Step 2: Calculate the number of votes cast According to the problem, only 63% of the registered voters cast their votes. Therefore, the number of votes cast is given by: \[ \text{Votes cast} = 0.63 \times x \] ### Step 3: Understand the ratio of votes received by the candidates The ratio of votes received by the two candidates is 4:5. Let the votes received by the first candidate be \( 4y \) and the votes received by the second candidate be \( 5y \). ### Step 4: Relate the votes to the winning candidate According to the problem, the winning candidate received 1120 votes. Since the winning candidate received \( 5y \) votes (as per the ratio), we can set up the equation: \[ 5y = 1120 \] ### Step 5: Solve for \( y \) Now, we can solve for \( y \): \[ y = \frac{1120}{5} = 224 \] ### Step 6: Calculate the votes received by both candidates Now we can find the votes received by both candidates: - Votes received by the first candidate: \[ 4y = 4 \times 224 = 896 \] - Votes received by the second candidate: \[ 5y = 5 \times 224 = 1120 \] ### Step 7: Calculate the total votes cast The total votes cast can be calculated as: \[ \text{Total votes cast} = 896 + 1120 = 2016 \] ### Step 8: Set up the equation for total votes cast We know from Step 2 that the total votes cast is also equal to \( 0.63x \). Therefore, we can set up the equation: \[ 0.63x = 2016 \] ### Step 9: Solve for \( x \) Now, we can solve for \( x \): \[ x = \frac{2016}{0.63} = 3200 \] ### Conclusion Thus, the total number of registered voters in the village is \( 3200 \). ---
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