यदि मापक सिलिंडरों की धारिताएँ 1 लीटर, 6 लीटर, 25 लीटर और 100 लीटर हैं, तो किसी टंकी से 298 लीटर पानी निकालने के लिए किसी को कम-से-कम कितनी बार मापने की आवश्यकता होगी?

Correct Option: (c) 9

We need to find the minimum number of times one needs to measure to get 298 litres of water from a tank using measuring cylinders of capacities 1 litre, 6 litres, 25 litres, and 100 litres. To minimize the number of measurements, we should use the largest possible cylinders first. Let's divide 298 by 100: 298 = 2 x 100 + 98 (2 measurements of 100L). Remaining = 98 litres. Now divide 98 by 25: 98 = 3 x 25 + 23 (3 measurements of 25L). Remaining = 23 litres. Now divide 23 by 6: 23 = 3 x 6 + 5 (3 measurements of 6L). Remaining = 5 litres. Now divide 5 by 1: 5 = 5 x 1 (5 measurements of 1L). Total number of measurements = 2 (from 100L) + 3 (from 25L) + 3 (from 6L) + 5 (from 1L) = 13 measurements? Wait, is there a way to do it in fewer measurements? Can we use subtraction or over-measuring? For example, 3 x 100 = 300 litres (3 measurements), and then subtract 2 litres using 1-litre cylinder twice (2 measurements), total 3 + 2 = 5 measurements! Let's check this greedy approach with over-measurement: 298 is close to 300 (which is 3 x 100). Take 3 measurements of 100L = 300L (3 times). Then measure out 2 litres using the 1L cylinder twice (-2L, 2 times). Total measurements = 3 + 2 = 5 times! Let's check if we can do it in 4 times: 3 x 100 = 300, and remove 2 using something else? No 2L cylinder exists (cylinders are 1, 6, 25, 100). So removing 2 requires two 1L measurements. Total = 3 + 2 = 5 measurements. Wait, let's check other options: (a) 4, (b) 5, (c) 9, (d) 13. Since 5 is available in option (b), let's verify if 4 is possible. To get 298 in 4 measurements: sum or difference of 4 cylinders. Max sum of 4 is 400. Can we get 298 with 4? No combination of 4 standard cylinder fillings/empties gives 298 with 4 operations. Thus 5 is the minimum.