In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?

### Concept & Logic This problem is solved using the absolute difference method between percentages on a common base. Because the total number of appeared candidates is identical for both State A and State B, we can directly subtract their selection percentages. The difference in these percentages will equal the absolute difference in the number of selected candidates. ### Step-by-step Solution **Given:** State A selection rate = 6% State B selection rate = 7% State B has 80 more selected candidates than State A. The number of appeared candidates is equal in both states. Let the total number of appeared candidates from each state be $x$. Calculate the number of selected candidates from each state in terms of $x$: Selected from State A = 6% of $x = 0.06x$ Selected from State B = 7% of $x = 0.07x$ We are given that State B had 80 more selections than State A. Set up the equation: $$ 0.07x - 0.06x = 80 $$ Simplify and solve for $x$: $$ 0.01x = 80 $$ $$ \frac{1}{100} \times x = 80 $$ $$ x = 80 \times 100 = 8000 $$ ### Exam Strategy & Shortcut Recognize the common base immediately. Since candidates in A = candidates in B, the 1% difference in selection rate (7% - 6%) directly corresponds to the 80 student difference. If 1% = 80 students, then 100% = 8000 students. No algebraic equations are necessary; this is a purely mental calculation. ### Common Pitfall A common error is overcomplicating the setup by introducing two separate variables (like $x$ and $y$) for the states before realizing the problem states they are equal. Always leverage the "equal number" constraint immediately to keep it a single-variable mental math problem. ### Final Answer **Therefore, the correct answer is 8000.**