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Let's solve the problem step by step.

### Given:
- 68 votes were declared invalid.
- The winning candidate got 52% of the valid votes and won by 98 votes.
- We need to find the total number of votes polled.

### Let:
- The total number of valid votes be \( x \).

The winning candidate got 52% of the valid votes, so:
- Votes for the winning candidate = \( 0.52x \).
- Votes for the other candidate = \( 0.48x \).

The difference between the votes of the two candidates is given as 98 votes:
\[
0.52x - 0.48x = 98
\]
\[
0.04x = 98
\]
\[
x = \frac{98}{0.04} = 2450
\]

Thus, the number of valid votes is 2450.

### Total number of votes polled:
The total number of votes polled includes both the valid and invalid votes:
\[
\text{Total votes} = 2450 + 68 = 2518
\]

### Answer:
The total number of votes polled was **2518** (Option D).

Would you like further details or have any other questions?

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Here are 5 related questions to expand your understanding:
1. How would the solution change if the winning margin were reduced to 50 votes?
2. What percentage of the total votes polled were declared invalid?
3. If the losing candidate had won, what would be the difference in the percentage of votes they received?
4. How does the concept of valid and invalid votes affect the total voter turnout?
5. Can you determine the exact number of votes each candidate received?

**Tip:** Always check if the problem involves invalid votes, as they don't affect the results but are part of the total votes.

In an election involving two candidates, 68 votes were declared invalid. The winning candidate got 52% of the valid votes and won by 98 votes. The total number of votes polled was:

Solve an election problem where the winning candidate secured 52% of valid votes and won by 98 votes. Learn how to calculate the total number of votes polled, including invalid votes, using algebraic methods and percentage concepts. Suitable for Grades 9-10 students.

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