Find the largest number which divides 55, 127 and 175 so as to leave the same remainder in each case?
a) 24
b) 20
c) 21
d) 25

Hint: We have given 3 numbers 55, 127 and 175. Do the subtraction of 55 and 127, 127 and 175, 55 and 175. Then take the HCF of what will remain from the subtraction of the 55 and 127, 127 and 175, 55 and 175. HCF is the answer.

Complete step-by-step answer:

In the above question, three numbers are given:

55, 127 and 175

Now, taking two numbers at a time then subtract these numbers and noted down the result of the three subtractions. We are showing the subtractions below:

127 – 55 = 72

175 – 127 = 48

175 – 55 = 120

Now, take the HCF of the above three results of subtraction. We are going to find the HCF (72, 48, 120).

Prime factorization of:

72 = 2×2×2×3×3

48 = 2×2×2×2×3

120 = 2×2×2×3×5

From the above prime factorization, we have seen the HCF (72, 48, 120) is 2×2×2×3 which is equal to 24.

Hence, the largest number which divides 55, 127 and 175 so as to leave the same remainder in each case is 24.

Hence, the correct option is (a).

Note: We can also get the correct option without solving using the above method by dividing the every option with all the three numbers and then see which option would be the largest number which on division gives the same remainder in each case.