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.