Two candidates were participating in an election. Of the total number of people in the electoral roll in that election, 10% did not use their votes and 60 votes were declared invalid. The winning candidate secured 47% of the total votes of the voter list and he won the election by 308 votes. How many votes were cast in that election?

# Two candidates were participating in an election. Of the total number of people in the electoral roll in that election, 10% did not use their votes and 60 votes were declared invalid. The winning candidate secured 47% of the total votes of the voter list and he won the election by 308 votes. How many votes were cast in that election?

1. A
6200
2. B
5580
3. C
6000
4. D
7200

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### Solution:

Let the two candidates be A and B.
Let the number of votes A get be x.
Now, B, gets 308 less votes therefore B gets = x−308
The total number of votes polled will be votes casted to A plus votes casted to B and then the 60 invalid votes:
x+x−308+60=2x−248
Given that 10% of the listed population refrained from voting , therefore 90% of the listed population took part in the election. Let the total population be P.
90% of P = 2x−248
$⇒P=2x-248×\frac{100}{90}=\frac{20x-2480}{9}$
47% of this population voted for A , since A got a total of x votes , therefore:
47% of $\frac{20x-2480}{9}$ = x
x = 2914
The total numbers of votes polled are 2x−248, i.e. 5580.

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