Question

The sum of the digits of a two-digit number is 9. When the digits are reversed, the number decreases by 27. Find the original number.

• A. 63
• B. 54
• C. 72
• D. 36

Answer 1

The Correct Option is A

Step 1: Let the number be \(10a+b\) with \(a+b=9\).
Step 2: Reversed number is smaller by 27: \((10a+b)-(10b+a)=27 \Rightarrow 9(a-b)=27 \Rightarrow a-b=3\).
Step 3: Solving \(a+b=9,\ a-b=3\): \(a=6,b=3\); number \(= 63\).

Quick Tip: Reversing a two-digit number changes it by \(9(a-b)\).