Question

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 ?​

Answer 1

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 2

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×$\frac{20}{100}$=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

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