In a competitive examination in State A, 6% of the candidates who appeared were selected. In State B, the same number of candidates appeared, but 7% of them were selected, and 80 more candidates were selected than in State A. How many candidates appeared from each State?

Introduction:
This question involves percentages and simple algebra. The same number of candidates appear for a competitive examination in two different states, but different percentages are selected, and the difference in the number of selected candidates is known. The goal is to find the total number of candidates who appeared from each state.

Given Data / Assumptions:
Let the number of candidates appearing from each state be N.
In State A, 6% of N candidates are selected.
In State B, 7% of N candidates are selected.
The number selected in State B exceeds the number selected in State A by 80 candidates.
We are to find N, the number of candidates from each state.

Concept / Approach:
We convert the percentage selections to algebraic expressions and then use the known difference in selected candidates to form an equation. Specifically, selected in State A is 0.06 * N, selected in State B is 0.07 * N, and their difference is 80. Solving this linear equation gives N directly.

Step-by-Step Solution:
Let N be the number of candidates appearing from each state. Number selected from State A = 6% of N = 0.06 * N. Number selected from State B = 7% of N = 0.07 * N. We are told that State B has 80 more selected candidates than State A. So 0.07 * N - 0.06 * N = 80. Simplify left side: (0.07 - 0.06) * N = 0.01 * N. Thus 0.01 * N = 80. Solve for N: N = 80 / 0.01 = 8000. Therefore, 8000 candidates appeared from each state.
Verification / Alternative check:
We can verify the answer by calculating actual selected numbers. For N = 8000, number selected in State A is 6% of 8000 = 0.06 * 8000 = 480. Number selected in State B is 7% of 8000 = 0.07 * 8000 = 560. The difference between 560 and 480 is 80 candidates, which matches the given condition. This confirms that N = 8000 is correct.

Why Other Options Are Wrong:
If N were 4000, the difference in selected candidates would be 1% of 4000 = 40, not 80. If N were 12000, the difference would be 120, and for 16000 it would be 160. For 20000, the difference would be 200. None of these match the specified difference of 80, so 8000 is the only consistent value.

Common Pitfalls:
A common mistake is to mix up the percentages or to add them incorrectly. Another error is forgetting that the same N applies to both states, leading to extra variables that make the problem seem more complex than it is. Keeping the algebra simple and focusing on the difference of percentages (1%) times N equalling 80 quickly leads to the correct solution.

Final Answer:
The number of candidates who appeared from each state is 8000.