Three candidates were participating in an election. The person in third place got 20% of the total votes while the difference between the votes of the winner and the first runner-up was 20% of the total votes. If the difference between the votes of the first runner-up and the second runner-up was 37,000, how many votes did the winner receive?

Given:

There are 3 candidates in the election.

The third-place candidate got 20% of the total votes.

The difference between the votes of the winner and the first runner-up was 20% of the total votes.

The difference between the votes of the first runner-up and the second runner-up was 37,000 votes.

Formula used:

Percentage = (Part / Whole) × 100

Total = Part1 + Part2 + Part3

Solution:

Let 100x be the total number of votes.

Let the winners get votes and the 2nd runner-up get b votes.

The number of votes for the third-place candidate is 20% of total votes = 20x.

So the total number of votes winner and 2nd runner-up gets is

a + b + 20x = 100x

a + b = 80x ..........(1)

According to the question.

The difference in the votes between votes of the winner and the first runner-up was 20% of the total votes

So,

a - b = 20x......... (2)

Solving equation (1) & (2),

We get a = 50x and b = 30x

Now, the difference between the votes of the first runner-up and the second runner-up was 37,000

So, 30x - 20x = 37000

x = 3700

The number of votes for the winner is 50x = 50 × 3700 = 1,85,000

Therefore, the winner received 1,85,000 votes.

Shortcut Trick

Let's assume that total votes = 100 unit

So, person in 3^rd place got 20% which is = 20 unit remaining 80 unit

Difference of votes of 1st and 2nd is 20%, so winner must got 50 unit and 2^nd got 30 unit

According to the question, the difference of votes between 2^nd and 3^rd is 37000

So,(30 - 20) = 10 unit → 37,000

So, 50 unit → 37000/10 × 50 = 37000 × 5 = 185000