In a two-candidate election 1401 votes were cast. If 30 voters had switched their votes from the winner to the loser, the loser would have won by 5 votes. How many votes did each candidate actually receive?

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Answer 1 · 2017-04-20T11:04:57

Winner got $728$ $728$ votes and loser got $673$ $673$ votes in the election.

Let Winner(W) got $w$ $w$ votes. and Loser(L) got $l$ $l$ votes.
$w + l = 1401$ $w+l=1401$ (1)

If $30$ $30$ votes had switched then $(l + 30) - (w - 30) = 5 or l - w = 5 - 60 or w - l = 55$ $(l+30) -(w-30) =5 or l-w = 5-60 or w-l=55$ (2)

Adding equation (1) and equation (2) we get $2w=1456 or w=728 :.l=1401-728 =673$

Winner got $728$ votes and loser got $673$ votes in the election. [Ans]