In a village there are 3990 registered voters. 70% of the registered voters could cast their votes and none of the votes were invalid. If only two candidates were contesting the el... In a village there are 3990 registered voters. 70% of the registered voters could cast their votes and none of the votes were invalid. If only two candidates were contesting the election and the respective ratio of the votes received by them is 12 : 7, what is the number of votes received by the winning candidate? Read more

Steps to Solve

1. Calculate the total votes cast To find out how many voters actually voted, we can use the following calculation: [ \text{Total votes cast} = \text{Total registered voters} \times \text{Percentage who voted} ] Substituting the given numbers: [ \text{Total votes cast} = 3990 \times 0.70 = 2793 ]

2. Determine the ratio of votes received by each candidate The votes received by the two candidates are in the ratio of 12:7. Let's denote the votes received by the winning candidate as (12x) and the votes received by the other candidate as (7x).

3. Set up the equation for total votes Since the total votes received must equal the total votes cast: [ 12x + 7x = 2793 ] Combining like terms gives: [ 19x = 2793 ]

4. Solve for (x) Now, divide both sides by 19 to find (x): [ x = \frac{2793}{19} = 147 ]

5. Calculate the votes received by the winning candidate Now, we can find the votes received by the winning candidate: [ \text{Votes received by winning candidate} = 12x = 12 \times 147 = 1764 ]