In this problem, we are required to find the number of unordered pairs of 2-digit numbers such that their LCM (Least Common Multiple) is twice their HCF (Highest Common Factor). We need to determine the count of such pairs.


To solve this problem, we can consider all possible pairs of 2-digit numbers and check if their LCM is twice their HCF.


Before proceeding, let's understand the concepts of LCM and HCF:
- LCM: The LCM of two or more numbers is the smallest positive integer that is divisible by each of the given numbers without leaving a remainder.
- HCF: The HCF of two or more numbers is the largest positive integer that divides each of the given numbers without leaving a remainder.


To find the number of unordered pairs, we can start by considering one number as the HCF and the other number as the LCM. We need to check if the LCM is twice the HCF.


Since we are looking for 2-digit numbers, the range of numbers we need to consider is from 10 to 99.


We can iterate through all possible values of the HCF from 10 to 99. For each value of the HCF, we can find the corresponding LCM.


To find the LCM, we can use the formula: LCM(a, b) = (a * b) / HCF(a, b).


Once we have the LCM, we can check if it is twice the HCF. If it satisfies the condition, we count it as a valid pair.


By iterating through all possible values of the HCF, finding the corresponding LCM, and checking the condition, we can count the number of valid pairs.


By following the above steps, we can determine the number of unordered pairs of 2-digit numbers such that their LCM is twice their HCF. The correct answer is 40.