Question

In an election, 15% of voters did not cast their votes and 20% of casted votes are invalid. If candidate A and B get the votes in the ratio 15 : 19. Candidate B gets 1600 votes more than A. There are 1500 transgender voters and all are voted to candidate A. Then find the percentage of transgender in total voters.

1. 15%
2. 7.5%
3. 7%
4. 10%
5. None of these

Answer 1

Correct Answer - Option 2 : 7.5%

Given:

Total number of transgender voters = 1500

Percentage of voters who did not cast their votes = 15%

Percentage of casted votes which are invalid = 20%

The ratio of votes get by candidate A and B = 15 : 19

Number of extra votes get by candidate B = 1600

Concept used:

Total number of voters = {Total number of casted votes/(100 – Percentage of voters did not cast their votes)} × 100

Calculation:

Let the votes get by candidate A and B is 15x and 19x respectively.

Then, 19x – 15x = 1600

⇒ 4x = 1600

⇒ x = 400

Total number of valid votes = (15 + 19) × 400

⇒ 34 × 400

⇒ 13600

Total number of casted votes = {13600/(100 – 20)} × 100

⇒ {13600/80} × 100

⇒ 170 × 100

⇒ 17000

Total number of voters in the village = {17000/(100 – 15)} × 100

⇒ {17000/85} × 100

⇒ 200 × 100

⇒ 20000

Percentage of transgender in total valid voters = (1500/20000) × 100

⇒ 150000/20000

⇒ 7.5%

∴ The transgender is 7.5% of total number of voters.