A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it and replaced by same quantity of liquid B. Again 4 litres of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?
Answer & explanation
Answer: (c) 16: 9
Each removal takes away 4/20 = 1/5 of whatever A is present, leaving 4/5 of it. After two rounds A = 20 × (4/5)² = 12·8 litres and B = 7·2 litres, a ratio of 16 : 9.
- After the first replacement: A = 20 − 4 = 16 litres.
- Second removal takes 1/5 of the mixture, so A falls to 16 × 4/5 = 12·8 litres.
- B = 20 − 12·8 = 7·2 litres.
- A : B = 12·8 : 7·2 = 128 : 72 = 16 : 9.
Remember · Repeated replace-and-remove: remaining original = initial × (1 − removed/total)ⁿ.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·