19 boys turn out for playing hockey. Of these, 11 are wearing hockey shirts and 14 are wearing hockey pants. There are no boys without shirts and/or pants. What is the number of boys wearing full uniform?
Answer & explanation
Answer: (c) 6
Every boy wears at least a shirt or pants, so adding shirts and pants counts the boys in full uniform twice. 11 + 14 − 19 = 6 boys wear both.
- Every one of the 19 boys wears a shirt, pants or both.
- Shirts + pants = 11 + 14 = 25, which counts the boys wearing both twice.
- Both = 25 − 19 = 6.
- Check: 5 with shirts only + 8 with pants only + 6 with both = 19.
Remember · For two overlapping groups that together cover everyone: both = first group + second group − total.
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). ·