there were two candidates in an election.10%of the member in the voter's list did not cast their votes and 50 votes were declared invalid . the successful candidates secured 308 votes more than his rival.if 47%of the total members voted in favor of successful candidates,then find the votes secured by each candidate?
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there were two candidates in an election.10%of the member in the voter's list did not cast their votes and 50 votes were declared invalid . the successful candidates secured 308 votes more than his rival.if 47%of the total members voted in favor of successful candidates,then find the votes secured by each candidate?
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Candidate A got m votes, Candidate B got n votes. Suppose B was successful.
invalid votes: 60 (note). for the value 50 - the problem does not work)
Total number of voters in the list = N
No Voting or absentees: N * 10/100 = 0.1 N
Total number of VALID votes = n+m
Total number of polled votes = (n+m+ 60) = 90% N = 0.9 N
So, n+m = 0.9 N - 60 --- equation 1
n = m + 308
n - m = 308 -- equation 2
Add eq 1 and eq 2:
2 n = 0.9 N + 308 - 60 = 0.9 N + 248
n = 0.45 N + 124 -- equation 3
n = 47 % N = 0.47 N -- equation 4
So, 0.45 N + 124 = 0.47 N
124 = 0.02 N
N = 6,200
n = 0.47 * 6,200 = 2,914
m = n - 308 = 2,606
invalid votes: 60 (note). for the value 50 - the problem does not work)
Total number of voters in the list = N
No Voting or absentees: N * 10/100 = 0.1 N
Total number of VALID votes = n+m
Total number of polled votes = (n+m+ 60) = 90% N = 0.9 N
So, n+m = 0.9 N - 60 --- equation 1
n = m + 308
n - m = 308 -- equation 2
Add eq 1 and eq 2:
2 n = 0.9 N + 308 - 60 = 0.9 N + 248
n = 0.45 N + 124 -- equation 3
n = 47 % N = 0.47 N -- equation 4
So, 0.45 N + 124 = 0.47 N
124 = 0.02 N
N = 6,200
n = 0.47 * 6,200 = 2,914
m = n - 308 = 2,606
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