the ratio of james' age to andy's age is 2:7. in 8 years' time,the ratio will become 2:5. find james' age present age

Let :

James' age now = x
Andy's age now = y

x : y = 2 : 7
or
7x = 2y

8 years from now, their age will be :
James' age = x + 8
Andy's age = y + 8

With the ratio of
(x + 8) : (y + 8) = 2 : 5


We can simplify the second term into
5(x + 8) = 2(y + 8)
5x + 40 = 2y + 16
5x - 2y = -24

Substitute the first term into the second one
5x - 2y = -24
5x - (7x) = -24
-2x = -24
x = 12

So, James' age now is 12 years old.