Explanation:

- The total number of registered voters is \( x \).

- 80% of voters cast their votes, so the number of votes cast is \( 0.8x \).

- Ram wins by 600 votes, which means Ram has 600 more votes than Shyam.

- If Ram had received 12.5% fewer votes, his votes would equal Shyam's.

- Let's denote Ram's votes as \( R \) and Shyam's votes as \( R - 600 \).

- According to the condition of reduction, \( 0.875R = R - 1200 \).

- Solving \( 0.875R = R - 1200 \), we find \( R = 4800 \).

- Therefore, \( R + (R - 600) = 0.8x\).

- Solving \( 4800 + 4200 = 0.8x \), gives \( x = 5250 \).

- Correct Answer: Option 2: 5250