In an election,a candidate score 77% votes and won by majority of 2160...
Calculation of Total Votes Cast in an Election
Given Data:
- Candidate scored 77% votes
- Won by a majority of 2160 votes
Solution:
Let's assume the total number of votes cast in the election is 'x'. So, the number of votes the candidate got is 77% of 'x' which is 0.77x.
As per the given data, the candidate won by a majority of 2160 votes. It means that the difference between the number of votes the candidate got and the number of votes the opponent got is 2160.
Let's assume the number of votes the opponent got is 'y'. So, the difference between the number of votes the candidate got and the number of votes the opponent got is:
0.77x - y = 2160
Now, we need to find the value of 'x' which represents the total number of votes cast in the election.
Let's rearrange the above equation:
0.77x = y + 2160
Dividing both sides by 0.77, we get:
x = (y + 2160) / 0.77
Now, we need to find the value of 'y' which represents the number of votes the opponent got.
As per the given data, the candidate scored 77% votes which means that the opponent got the remaining 23% votes.
So, the number of votes the opponent got is:
y = 0.23x
Now, substitute the value of 'y' in the equation of 'x' to get the total number of votes cast in the election:
x = (0.23x + 2160) / 0.77
Multiplying both sides by 0.77, we get:
0.77x = 0.23x + 2160
Subtracting 0.23x from both sides, we get:
0.54x = 2160
Dividing both sides by 0.54, we get:
x = 4000
Conclusion:
The total number of votes cast in the election is 4000.