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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2014-08-25T21:57:23+05:30

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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

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