Answer :
Final answer:
The numbers B. 84 and 96 are the correct pair as they both have an H.C.F. of 12 and a difference of 12, meeting the conditions specified in the question.
Explanation:
The question asks to find a pair of numbers whose Highest Common Factor (H.C.F.) is 12, and their difference is also 12. Since H.C.F. is a factor, both numbers must be multiples of 12. We will use this information to evaluate each pair of numbers provided in the options.
- A. 70, 84: The difference is 14, which fails the requirement of a 12 difference. Also, 70 is not a multiple of 12.
- B. 84, 96: The difference is 12, which fits the requirement, and both numbers are multiples of 12 (84 = 7 imes 12, 96 = 8 imes 12). This pair satisfies both conditions.
- C. 66, 77: The difference is 11, not matching the 12 difference condition. Additionally, neither number is a multiple of 12.
- D. 80, 92: The difference is 12, which fits the requirement, but 80 is not a multiple of 12.
Therefore, the pair that has both a difference of 12 and an H.C.F. of 12 is option B. 84, 96.
