In an election, 30% of the voters voted for candidate A whereas 60% of the remaining voted for candidate B. The remaining voters did not vote. If the difference between those who voted for candidate A and those who did not vote was 1200, how many individuals were eligible for casting vote in that election?

### Concept & Logic This is a fractional distribution problem. When a percentage is taken from the "remaining" amount, you must subtract the previously allocated portions from the total before calculating the new share. $$ \text{Remaining} = \text{Total Base} - \text{Allocated Share} $$ ### Step-by-Step Solution * **Given:** * Candidate A gets 30% of total voters. * Candidate B gets 60% of the *remaining* voters. * Difference between A and non-voters = 1200. * **Deduction:** * Let the total number of eligible voters be 100 units. * Votes for Candidate A = 30 units. * Remaining voters = 100 - 30 = 70 units. * Votes for Candidate B = 60% of 70 = 42 units. * Voters who did not vote = Remaining from the 70 after Candidate B's share = 70 - 42 = 28 units. * Difference between Candidate A and non-voters = 30 units - 28 units = 2 units. * We are given that this difference is 1200 individuals. * 2 units = 1200, which means 1 unit = 600. * Total eligible voters (100 units) = $100 \times 600 = 60,000$. ### Exam Strategy & Shortcut Use a branching tree method to track the percentages mentally. $100 \rightarrow A (30)$, Remaining (70). $70 \rightarrow B (60\% \text{ of } 70 = 42)$, Non-voters (28). Compare A (30) and Non-voters (28). The difference is 2%. If 2% of the total equals 1200, then 1% equals 600. Multiply by 100 to get the total $100\% = 60,000$. ### Common Pitfall The most frequent mistake is calculating Candidate B's share as 60% of the *total* voters instead of the *remaining* 70%. This breaks the mathematical model and leads to incorrect unit comparisons. ### Final Answer **Therefore, the correct answer is 60,000.**