If two numbers with HCF 9 are in the ratio 5 : 7, what is their difference?

Correct option is A

Given:

The two numbers are in the ratio 5:7, and their HCF is 9.

Concept Used:
Let the two numbers be ( 5x ) and ( 7x ), where ( x ) is a common multiple.

Since the HCF of the two numbers is 9, we have:

​$$\text{HCF}(5x, 7x) = x = 9$$​​

Solution:
Substitute ( x = 9) into the expressions for the two numbers:

​$$5x = 5 \times 9 = 45\\\ \\7x = 7 \times 9 = 63$$​​

The difference between the two numbers is:

63 - 45 = 18

Therefore, the difference between the two numbers is 18.