A number consists of three digits of which the middle one is zero and their sum is 4. If the number formed by interchanging the first and last digits is greater than the number itself by 198, then the difference between the first and last digits is
Answer & explanation
Answer: (b) 2
Swapping the first and last digits of a three-digit number changes it by 99 × (difference of those digits). 198 ÷ 99 = 2, so the digits differ by 2 — the number is 103, which becomes 301.
- Let the number be 100a + c (middle digit 0); interchanged, it is 100c + a.
- (100c + a) − (100a + c) = 99(c − a) = 198, so c − a = 2.
- With a + c = 4: a = 1 and c = 3, so the number is 103.
- Check: 301 − 103 = 198.
Remember · Interchanging the end digits of a three-digit number changes it by 99 × their difference; divide the change by 99.
Question and answer: UPSC's official GS Paper II (2018, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·