RRB NTPC Mains or Stage 2 Model Paper 9 with solutions

(b) Let x be the remainder, then the numbers(55 – x), (127 – x) and (175 – x) are exactly divisible by the required number.
Now, we know that if two numbers are divisible by a certain number, then their difference is also divisible by the number.
Hence the numbers (127 – x) – (55 – x), (175– x) – (127 – x) and (175 – x) – (55 – x) or, 72,
48 and 120 are divisible by the required number. HCF of 48, 72 and 120 = 24,therefore the required number = 24.