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?
- (a) 4
- (b) 5 ✓ UPSC's answer
- (c) 9
- (d) 13
Why the answer is (b)
• Measuring can mean filling a cylinder from the tank or taking water back out with a cylinder.
• Only adding: 298 = 2 × 100 + 3 × 25 + 3 × 6 + 5 × 1, which takes 13 measurements.
• Using removal: fill the 100-litre cylinder 3 times (300 litres) and take out 1 litre twice: 300 − 2 = 298, in 5 measurements.
• Four measurements cannot work: three 100s leave −2, which no single cylinder gives, and two 100s leave 98, which no two cylinders give. So the minimum is 5: (b).
Why the other options are wrong
- (a) 4
- No combination of four measurements gives exactly 298 litres.
- (c) 9
- 9 is not the minimum; 3 × 100 − 2 × 1 takes only 5.
- (d) 13
- 13 counts only additions; taking water out reduces it to 5.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.