The answer lies in the second statement. If the two number has HCF 15, it means both numbers have factors of 15.

Study this list: 15,30,45,60,75.

These are the possible numbers since they are numbers less than 90 with factors 15.

Identify the numbers yourself.

HCF = 15 = 3 × 5

This means they are multiples of 15. They are also less than 90 (given in question)

Each number has at least one prime factor 3 and one prime factor 5.

And they have a maximum of one prime factor 3 and one prime factor in common. They have no other prime factors in common.



Possible numbers :

15
15 × 2 = 30
15 × 3 = 45
15 × 2² = 15 × 4 = 60
15 × 5 = 75

Out of these, 30 and 60 are eliminated since their HCF would be 5 × 3 × 2 = 30

They have a prime factor 2 in common.


We are left with 15,45,75.


Given that their sum is 120 and difference less than 70, there is only one possible option of the two numbers.


It should be obvious from here.