If p : q = 6:5, then what is the value of (6p + 5q) : (6p-5q)?

Given: 

p : q = 6 : 5 

To find: (6p + 5q) : (6p - 5q)

Solution: 

Let p = 6k , q = 5k 

Putting this in the expression;

 $$=\frac{6(6k)+5(5k)}{6(6k)-5(5k)} \\ \ \\ = \frac{36k + 25k}{36k - 25k} \\ \ \\ = \frac{61k}{11k} \\ \ \\ = \frac{61}{11}$$ 

Thus, the value of  (6p + 5q) : (6p - 5q) = 61 : 11