What is the minimum number of times one needs to measure to get 298 litres of water from a tank, if the measuring cylinders have capacities 1 litre, 6 litres, 25 litres and 100 litres?
Answer & explanation
Answer: (b) 5
Measuring can remove water as well as add it: take 100 litres three times (300 litres) and take out 1 litre twice. That is 5 measurements, and 4 cannot work because 298 is 2 short of 300 and no single cylinder holds 2 litres.
- 298 = 300 − 2 = 100 + 100 + 100 − 1 − 1: three fills of 100 litres and two removals of 1 litre = 5 measurements.
- Could 4 work? With at most two 100-litre fills, the other two measures add at most 50 litres: 250 < 298.
- So three 100-litre fills are needed, leaving one measure to remove exactly 2 litres — impossible with 1, 6, 25 or 100.
- Minimum = 5.
- Check: the greedy pour-in-only count 2 × 100 + 3 × 25 + 3 × 6 + 5 × 1 = 13 measures is the trap option.
Remember · For 'minimum measurements', aim just above the target with the big measure, then remove the excess.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·