Correct Answer - Option 1 : 2
Given:
Sum of those two numbers is 120 and HCF of them is 12
Concept Used:
HCF (Highest Common Factor): HCF of x and y is the highest common factor which can divide x and y exactly
For Example,
12 → Factors of 12 are 1, 2, 3, 4, 6 and 12
16 → Factors of 16 are 1, 2, 4, 8 and 16
Here common factors are 1, 2 and 4. But of these 4 is the largest/highest
∴ HCF of 12 and 16 is 4
Calculation:
HCF of those two numbers are 12
Let, those numbers are 12x and 12y [Where x and y are prime to each other]
Accordingly,
12x + 12y = 120
⇒ 12(x + y) = 120
⇒ (x + Y) = 10
We can represent 10 as the sum of two numbers as
10 = 1 + 9
10 = 2 + 8
10 = 3 + 7
10 = 4 + 6
10 = 5 + 5
From the above, we can see that only (1,9) and (3,7) are prime to each other
∴ Such two pair of number can be there.
