There are certain 2-digit numbers. The difference between the number and the one obtained on reversing it is always 27. How many such maximum 2-digit numbers are there?
Answer & explanation
Answer: (d) None of the above
A 2-digit number and its reverse differ by 9 × (difference of the digits), so the digits must differ by 3. That gives 41, 52, 63, 74, 85, 96 and 14, 25, 36, 47, 58, 69 (and 30, if 03 is allowed) — at least 12 numbers, far more than 3, 4 or 5.
- (10a + b) − (10b + a) = 9(a − b), which is 27 in size when the digits differ by 3.
- Tens digit 3 more than units: 41, 52, 63, 74, 85, 96 (and 30, if its reverse 03 = 3 is accepted).
- Tens digit 3 less than units: 14, 25, 36, 47, 58, 69.
- That is 12 numbers (13 counting 30); even one direction alone gives 6. None of 3, 4 or 5 fits.
Remember · Number − reverse = 9 × (digit difference). Divide the given difference by 9 to get the digit gap, then list the pairs.
Question and answer: UPSC's official GS Paper II (2017, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·