Reversing a two-digit number — Aptitude Question
Reversing a two-digit number: A two-digit number has digits summing to 9. Reversing the digits gives a number 27… Answer and worked solution on CodeKairo.
- Topic: Mathematical Reasoning
- Section: Logical Reasoning
- Difficulty: Hard
- Time target: 120 seconds
Question
A two-digit number has digits summing to 9. Reversing the digits gives a number 27 less than the original. What is the number?
Options
- 45
- 54
- 63
- 72
Show the answer and the worked solution
Correct answer: C. 63
Worked solution
- Let the number be 10t + u with t + u = 9.
- Original − reversed = (10t + u) − (10u + t) = 9(t − u) = 27, so t − u = 3.
- Solving t + u = 9 and t − u = 3 gives t = 6, u = 3.
- The number is 63.
Answer: 63.
The idea
Reversing a two-digit number always changes it by 9 times the difference of the digits. That fact turns the puzzle into two simple equations.
Shortcut. Every option's digits already sum to 9, so just test the drop on reversal: 63 − 36 = 27, while 54 − 45 = 9 and 72 − 27 = 45.
Common trap. "72" — its reversal is literally 27, the number in the question, but 72 − 27 = 45, not a drop of 27.