there were two candidates in election 20% of the numbers in the voters list did not cast their votes and 50% votes were declared invalid . The succesful candidate secured 300 votes more than his rival . If45% of the total members voted in favour of successful candidate then find the vote secured by each candidate ?
Answers
Let first candidate got m votes and other candidate was successful and got n votes.
Invalid votes :60
Total number of voters in the list =N
No Voting or absentees:N×
100
20
=0.2 N
Total number of VALID votes =n+m
Total number of polled votes =(n+m+60)=80% of N=0.8N
So,
n+m=0.8N−50 ......(1)
n=m+300
n−m=300 ......(2)
On adding equation (1) and (2), we get
2n=0.8N+300−50⇒0.8N+250
n=0.40N+125 ......(3)
n=45% of N=0.45N ......(4)
0.40N+125=0.45N [from equation (3)]
125=0.05N
Hence,
Total votes N=2,500
Successful candidate got n=0.45×2,500⇒1,125 votes
First candidate got m=1,125−300⇒825 votes.
Answer:
Successful candidate got 1,125 votes
First candidate got 825 votes
Step-by-step explanation:
Let first candidate got m votes and other candidate was successful and got n votes.
Invalid votes :60
Total number of voters in the list =N
No Voting or absentees: N×=0.2N
Total number of VALID votes =n+m
Total number of polled votes =(n+m+60)=80% of N=0.8N
So,
n+m=0.8N−50 ......(1)
n=m+300
n−m=300 ......(2)
On adding equation (1) and (2), we get
2n=0.8N+300−50⇒0.8N+250
n=0.40N+125 ......(3)
n=45% of N=0.45N ......(4)
0.40N+125=0.45N [from equation (3)]
125=0.05N
Hence,
Total votes N=2,500
Successful candidate got n=0.45×2,500⇒1,125 votes
First candidate got m=1,125−300⇒825 votes
MARK ME BRAINLIEST