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UPSC CSE 2026 · PYQ · Logical Reasoning / Optimization · medium

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?

  1. A.4
  2. B.5✓ Correct
  3. C.9
  4. D.13

Explanation

We want to obtain 298 litres using measurements of capacity 1, 6, 25, and 100. Use the largest containers: 100 × 2 = 200 (2 measurements), 25 × 3 = 75 (3 measurements). Total so far = 275 in 5 measurements. Remaining = 23. 23 = 25 - 6 + ... requires more measurements. Try alternative: 100 × 2 = 200, then 25 × 4 = 100 making 300, then subtract 1 + 1 = 2 (impossible to subtract by adding). Better: use combination — 100 + 100 + 100 = 300, then return 1 + 1 = 2: total 5 measurements (3 pours + 2 removals = 5). 300 - 2 = 298. So minimum is 5 measurements.
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