correct answer is: a) 65 and 91

Explanation

Here, The ratio of two numbers be 5\;:\;7\;.
Their HCF be 13
We know, HCF is the highest common factor of two numbers.
So that, the numbers are :
\left(5\times13\right)=65
\left(7\times13\right)=91
Ans: The numbers are 65 and 91.

Other variants of this particular math question are:

1. Find the numbers given their ratio is 5 : 7 and their highest common factor (HCF) is 13.
2. Given that the ratio of two numbers is 5 : 7 and their highest common factor (HCF) is 13, ascertain the numbers.
3. If the ratio of two numbers is 5 : 7 and their highest common factor (HCF) is 13, what are the numbers?