In a village three people contested for the post of village Pradhan. Due to their own interest, all the voters voted and no vote was invalid. The losing candidate got `30%` votes. What could be the minimum absolute margin of votes by which the winning candidate led the nearest rival, if each candidate got an integral per cent of votes?

Options

A. 4
B. 2
C. 1
D. 3

Answer

To solve the problem, we need to determine the minimum absolute margin of votes by which the winning candidate led the nearest rival, given that one candidate received 30% of the votes.

### Step-by-Step Solution:

1. **Identify the Votes Distribution**:
- Let the total number of votes be represented as 100 (for simplicity, since we are dealing with percentages).
- The losing candidate received 30% of the votes. Therefore, the votes received by the losing candidate (C3) = 30 votes.

2. **Calculate Remaining Votes**:
- The remaining votes after the losing candidate's votes = 100 - 30 = 70 votes.
- These 70 votes will be divided between the two remaining candidates (C1 and C2).

3. **Assign Votes to Candidates**:
- Let C1 be the winning candidate and C2 be the nearest rival.
- Since C1 and C2 must receive integral percentages of the remaining 70 votes, we can express their votes as:
- C1 = x%
- C2 = y%
- Therefore, we have: x + y = 70 (where x and y are the votes received by C1 and C2 respectively).

4. **Determine the Percentages**:
- Since C1 must have more votes than C2, we can express C1's votes as:
- C1 = 36% (for example)
- C2 = 34%
- This satisfies the condition that both x and y are integral percentages.

5. **Calculate the Margin**:
- The margin of victory (M) is given by the difference between the votes received by C1 and C2:
- M = C1 - C2 = 36 - 34 = 2 votes.
- This is the minimum margin possible while ensuring that all candidates have integral percentages of votes.

### Conclusion:
The minimum absolute margin of votes by which the winning candidate led the nearest rival is **2 votes**.