In an election there were four candidate,5/6 of the electors voted for the winner.The runner up received 4/7 of the remaining votes.The third candidates received twice the vote of the fourth candidate.if the winner received 3021 votes more than the runner up ,how many electors voted

Answer 1

Let the total number of electors be x.
1st candidate (winner) received (5/6)*x votes
Remaining votes = x - (5/6)*x = (1/6)*x
2nd candidate (runner up) received (4/7)*(1/6)*x votes
3rd candidate received 2 times the votes of 4th candidate, so 3rd candidate received 2*(1/6)*x votes and 4th candidate received (1/6)*x votes.
Given that the winner received 3021 votes more than the runner up, we can write the equation:
(5/6)*x = (4/7)*(1/6)*x + 3021
Multiplying both sides by 42 to eliminate the fractions:
35x = 4x + 127482
Subtracting 4x from both sides:
31x = 127482
Dividing both sides by 31:
x = 4110
Therefore, the total number of electors who voted is 4110.