The sum of a two-digit number and the number obtained by reversing the digits is $66$. If the digits of the number differ by $2$, find the number.
Step-by-Step Solution
Key Concept: Number $= 10x + y$. Reverse $= 10y + x$. $(10x+y) + (10y+x) = 11(x+y) = 66 \Rightarrow x + y = 6$. Given $|x - y| = 2$.
$11(x + y) = 66 \Rightarrow x + y = 6$. [0.5 Mark]
Case 1: $x - y = 2 \Rightarrow 2x = 8 \Rightarrow x = 4, y = 2 \Rightarrow$ Number is $42$. [1.0 Mark]
Case 2: $y - x = 2 \Rightarrow 2y = 8 \Rightarrow y = 4, x = 2 \Rightarrow$ Number is $24$. Numbers are $42$ or $24$. [0.5 Mark]
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🎯 Official CBSE Marking Scheme:
Deriving $x + y = 6$: 0.5 Mark
Solving $x = 4, y = 2$ (Number 42): 1.0 Mark
Solving $x = 2, y = 4$ (Number 24): 0.5 Mark
Correct Answer: