Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p × q = 2430, then what is the difference between p and q?
Answer & explanation
Answer: (d) 9
2430 = 45 × 54, and 54 is 45 with its digits reversed. The difference between them is 54 − 45 = 9.
- 2430 = 2 × 3⁵ × 5; look for a two-digit factor whose reverse is the other factor.
- 2430 = 45 × 54, and 54 is 45 reversed.
- Difference = 54 − 45 = 9.
- Check: a two-digit number and its reverse differ by 9 × (difference of the digits) = 9 × (5 − 4) = 9.
Remember · A two-digit number minus its reverse = 9 × (difference of its digits).
Question and answer: UPSC's official GS Paper II (2022, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·