Two candidates contested from a constituency in an election. The winner secured `68%` of the votes polled. If the difference between their votes was 23,040, find the voes secured by the winner.

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step-by-Step Solution:

1. **Let the total votes be \( x \)**:
- We denote the total number of votes polled in the election as \( x \).

**Hint**: Define the total votes as a variable to simplify calculations.

2. **Votes secured by the winner**:
- The winner secured 68% of the total votes, which can be expressed as:
\[ \text{Votes secured by winner} = \frac{68}{100} \times x = 0.68x \]

**Hint**: Convert the percentage into a decimal to calculate the votes.

3. **Votes secured by the loser**:
- The loser secured the remaining votes, which is 32% of the total votes:
\[ \text{Votes secured by loser} = \frac{32}{100} \times x = 0.32x \]

**Hint**: Remember that the sum of the percentages of votes secured by both candidates should equal 100%.

4. **Set up the equation for the difference in votes**:
- According to the problem, the difference between the votes secured by the winner and the loser is 23,040. We can write this as:
\[ 0.68x - 0.32x = 23,040 \]

**Hint**: Use the information about the difference in votes to form an equation.

5. **Simplify the equation**:
- Simplifying the left side gives:
\[ 0.36x = 23,040 \]

**Hint**: Combine like terms to simplify the equation.

6. **Solve for \( x \)**:
- To find \( x \), divide both sides by 0.36:
\[ x = \frac{23,040}{0.36} \]
- Calculating this gives:
\[ x = 64,000 \]

**Hint**: When dividing, ensure you maintain the decimal places correctly.

7. **Calculate the votes secured by the winner**:
- Now that we have the total votes, we can find the votes secured by the winner:
\[ \text{Votes secured by winner} = 0.68 \times 64,000 \]
- This calculation results in:
\[ \text{Votes secured by winner} = 43,520 \]

**Hint**: Multiply the percentage of votes by the total to find the winner's votes.

### Final Answer:
The votes secured by the winner is **43,520**.