RRB ALP CBT I 13 Feb 2026 Shift 1 Paper

Concept:The division of fractions is converted into multiplication, and the identity $a^2 - b^2 = (a - b)(a + b)$ is used to simplify the expression.Explanation:Given $x : y = 9 : 11$, let $x = 9k$ and $y = 11k$.The given expression is $\frac{\frac{x+1}{y+1}}{\frac{x^2-1}{y^2-1}}$.Rewrite the division as multiplication:$\frac{x+1}{y+1} \times \frac{y^2-1}{x^2-1}$.Factorise both differences of squares:$y^2 - 1 = (y - 1)(y + 1)$ and $x^2 - 1 = (x - 1)(x + 1)$.So the expression becomes $\frac{x+1}{y+1} \times \frac{(y-1)(y+1)}{(x-1)(x+1)}$.Cancel the common factors $(x+1)$ and $(y+1)$ from the numerator and denominator.This simplifies to $\frac{y-1}{x-1}$.Substitute $x = 9k$ and $y = 11k$:$\frac{11k-1}{9k-1}$.Answer:Option C: $\frac{11k-1}{9k-1}$