Answer :
Final answer:
Only the pair 84 and 96 has an H.C.F of 12 and a difference of 12, satisfying the conditions of the question. The correct answer is option B.
Explanation:
The highest common factor (H.C.F) of two numbers means the largest number that can exactly divide both of them without leaving a remainder. If two numbers have their H.C.F as 12, it implies both numbers must be multiples of 12. Additionally, their difference also being 12 means that one of the numbers when divided by 12 would yield a quotient exactly 1 more than the quotient of the other number when divided by 12.
Now, let's examine the given pairs of numbers to check which pair meets both conditions:
- 70 and 84: The difference is 84 - 70 = 14, which doesn't meet the required difference of 12.
- 84 and 96: The difference is 96 - 84 = 12, and both are multiples of 12. This pair meets the conditions.
- 66 and 77: The difference is 77 - 66 = 11, and neither are multiples of 12.
- 80 and 92: The difference is 92 - 80 = 12, but 80 is not a multiple of 12.
Therefore, the only pair of numbers that have an H.C.F of 12 and a difference of 12 is 84 and 96.
