# 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?

Apr 20, 2017

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

#### Explanation:

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

If $30$ votes had switched then $\left(l + 30\right) - \left(w - 30\right) = 5 \mathmr{and} l - w = 5 - 60 \mathmr{and} w - l = 55$(2)

Adding equation (1) and equation (2) we get $2 w = 1456 \mathmr{and} w = 728 \therefore l = 1401 - 728 = 673$

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