A is a 2-digit number with different digits. B is also a 2-digit number and is obtained by reversing the digits of A. If A − B is…

Quantitative Aptitude ·Previously asked in UPSC Civil Services Examination 2026

View the full solved paper: GS Paper II

Question

A is a 2-digit number with different digits. B is also a 2-digit number and is obtained by reversing the digits of A. If A − B is a multiple of 27, where A B, how many such different A's are possible?

  1. A. 6
  2. B. 9 (Correct answer)
  3. C. 12
  4. D. 18

Correct Answer

Option B — 9

Detailed Solution & Explanation

The correct answer is Option B (9).

Key Points

  • If A = 10x + y then B = 10y + x and A − B = 9(x − y). For this to be a multiple of 27, (x − y) must be a multiple of 3, so x − y ∈ {3, 6, 9} (with A > B ⇒ x > y).
  • B must also be a genuine 2-digit number, so y ≠ 0.

Additional Information

  • Counting valid (x, y): x − y = 3 gives 6 pairs, x − y = 6 gives 3 pairs, x − y = 9 gives none (needs y = 0). Total = 9 → Option B.