Three persons A, B and C are standing in a queue not necessarily in the same order. There are 4 persons between A and B, and 7 persons between B and C. If there are 11 persons ahead of C and 13 behind A, what could be the minimum number of persons in the queue?
Answer & explanation
Answer: (a) 22
C is 12th from the front, so B is 4th or 20th, and A is then 9th, 15th or 25th. With 13 people behind A, the queue has A’s place + 13 people, which is smallest when A is 9th: 22.
- 11 persons are ahead of C, so C is 12th from the front.
- 7 persons between B and C means B is 8 places from C: 4th or 20th.
- 4 persons between A and B means A is 5 places from B: if B is 4th, A is 9th; if B is 20th, A is 15th or 25th.
- 13 persons are behind A, so the queue has (A’s place + 13) persons: 22, 28 or 38.
- The minimum is 22, with B 4th, A 9th and C 12th.
- Check: between B (4th) and A (9th) stand places 5–8, i.e. 4 persons; between B (4th) and C (12th) stand places 5–11, i.e. 7 persons; behind A (9th) stand places 10–22, i.e. 13 persons.
Remember · Queue items: ‘k persons between’ means a gap of k + 1 places; list the cases and take the minimum.
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). ·