SSC GD Constable 4 Feb 2025 Shift 1 Paper

Let the numbers be 11 x and 11 y , where x and y are co-prime integers.
Sum of numbers $=11\mathit{x}+11\mathit{y}$
Difference of numbers $=|11\mathit{x}-11\mathit{y}|$
Calculation:
$11\mathit{x}+11\mathit{y}=132$
$\Rightarrow 11\left(\mathit{x}+\mathit{y}\right)=132$
$\Rightarrow \mathit{x}+\mathit{y}=132∕11=12$
Possible co-prime pairs $\left(\mathit{x},\mathit{y}\right)$ such that $\mathit{x}+\mathit{y}=12$ are $\left(1,11\right)$ and $\left(5,7\right)$.
Case 1: $\mathit{x}=1,\mathit{y}=11$
Numbers are $11\times 1=11$ and $11\times 11=121$. ( 11 is not $>42$, so this case is rejected)
Case 2: $\mathit{x}=5,\mathit{y}=7$
Numbers are $11\times 5=55$ and $11\times 7=77$. (Both are $>42$ )
Difference $=|55-77|$
⇒ Difference $=|-22|$
⇒ Difference $=22$