The sum of a two-digit number and the number obtained by reversing its digits is $66$. The digits differ by $2$. Find the number(s).
Step-by-Step Solution
Key Concept: Let the digits be $x$ (tens) and $y$ (units); form and solve a pair of linear equations.
Let the tens digit be $x$ and units digit be $y$. Number $=10x+y$, reversed number $=10y+x$. Given: $(10x+y)+(10y+x)=66\Rightarrow 11x+11y=66\Rightarrow x+y=6$. [1.0 Mark]
Also given the digits differ by $2$: $x-y=2$ (taking $x>y$). [1.0 Mark]
Adding: $2x=8\Rightarrow x=4,\ y=2$. So the number is $42$ (or, taking $y-x=2$ instead, the number would be $24$). [1.0 Mark]
Correct Answer: