The recurring decimal representation 1.272727... is equivalent to

1. **Decompose the Number**: First, let's look at the number 1.272727... simply as $1 + 0.272727...$ This allows us to focus only on the decimal part. This approach of handling integers and decimals separately is a helpful mental math tactic [1].\n\n2. **Apply the Rule of 9s**: We see the digits '27' repeating. In aptitude exams, there is a standard shortcut: if two digits repeat, you place them over 99. \n So, $0.2727... = 27/99$.\n\n3. **Simplify the Fraction**: This is the most crucial step. A quick look tells us both 27 and 99 are divisible by 9. \n - $27 ÷ 9 = 3$\n - $99 ÷ 9 = 11$\n So, $27/99$ simplifies to $3/11$. \n *Note: This skill of rapid simplification is exactly what was tested in the 2014 and 2016 exams [18] [28], where reducing fractions revealed the answer instantly.*\n\n4. **Reconstruct**: Now, bring the integer '1' back.\n Total = $1 + 3/11$.\n\n5. **Convert to Improper Fraction**: \n $1 + 3/11 = (11 + 3) / 11 = 14/11$.\n\nThis matches Option (B) perfectly.