Five years ago, the ratio of David and his brother’s age was 3 : 2. Ten years hence, the ratio of their ages will be 6:5. What is David’s brother’s present age?

Let's denote David's age five years ago as 3x and his brother's age five years ago as 2x.

According to the problem, ten years from now, the ratio of their ages will be 6:5. This means that David's age in ten years will be 6y and his brother's age in ten years will be 5y.

But we also know that David's age in ten years is his age five years ago plus 15 (because 10 years from now is 15 years from five years ago). The same applies to his brother's age.

So we can set up the following equations:

3x + 15 = 6y (equation 1)

2x + 15 = 5y (equation 2)

We can solve these two equations simultaneously to find the values of x and y.

Subtract equation 2 from equation 1, we get:

x = y

Substitute y = x into equation 1, we get:

3x + 15 = 6x

This simplifies to:

3x = 15

So, x = 5.

Substitute x = 5 into 2x + 15 = 5y, we get:

10 + 15 = 5y

25 = 5y

So, y = 5.

Therefore, David's brother's age five years ago was 2x = 2*5 = 10 years old.

So, David's brother's present age is 10 + 5 = 15 years old.