10 years ago, the ratio of ages of A and B was in the ratio 7:10. 6 years hence, their ages will be in the ratio 5:6. What is the difference of their ages?

To solve this problem, we need to set up two equations based on the information given and then solve them simultaneously.

Let's denote the current ages of A and B as 'a' and 'b' respectively.

From the first statement, "10 years ago, the ratio of ages of A and B was in the ratio 7:10", we can write the equation:

(a - 10) / (b - 10) = 7 / 10

From the second statement, "6 years hence, their ages will be in the ratio 5:6", we can write the equation:

(a + 6) / (b + 6) = 5 / 6

Now we have a system of two equations. We can solve this system by either substitution or elimination method to find the values of 'a' and 'b'. Once we have the values of 'a' and 'b', we can find the difference of their ages by subtracting the smaller one from the larger one.