In an election a candidate who received 30 percent of the total votes cast was defeated by 15000 votes. Find the number of votes obtained by the winning candidate?

11250

15000

26250

37500

Explanation

Let the total number of votes be X.

The losing candidate received 30% of the total votes, which means:

$30/100 X = 0.3 X$

The winning candidate received 15000 votes more than the losing candidate, so:

$Winning candidate’s votes = 0.3 X + 15000$

Since the total votes are shared between these two candidates (assuming no invalid votes), the winning candidate must have received 70% of the total votes because:

$Winning candidate’s votes = 100% - 30% = 70% = 0.7 X$

Thus, we equate:

$0.7 X = 0.3 X + 15000$

Solving for X:

$0.7 X - 0.3 X = 15000$ $0.4 X = 15000$ $X = 15000/ 0.4 = 37500$

Now, the winning candidate received:

$0.7 \times 37500 = 26250$