A two-digit number has digit sum $9$. If digits reversed, the number increases by $9$. Original number is

A two-digit number has digit sum $9$. If digits reversed, the number increases by $9$. Original number is
  1. $45$
  2. $54$
  3. $36$
  4. $63$

Solution

Digits $a, b$, $a+b=9$. Reversed - original $= 9(b-a) = 9 \Rightarrow b-a = 1$. So $a=4, b=5 \Rightarrow 45$.

Asked in: IMO

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