Explanation:

- The total votes polled are 'y'.

- 40% of these votes are invalid, leaving 60% as valid votes.

- The winning candidate received 60% of the valid votes.

- The losing candidate received the rest of the valid votes.

- The winning margin was 6000 votes.

Let's calculate:

1. Invalid votes: 40% of 'y' = 0.4y

2. Valid votes: 60% of 'y' = 0.6y

3. Winning candidate votes: 60% of valid votes = 0.6 x 0.6y = 0.36y

4. Losing candidate votes: Remaining valid votes = 0.6y - 0.36y = 0.24y

5. Difference in votes = 0.36y - 0.24y = 0.12y = 6000

Calculate 'y':

$$0.12y=6000$$

$$y=6000/0.12=50000$$

- Option 2: 50000 is correct.