4 years ago, the ratio of 1/2 of A’s age that time and four times of B’s age at the time were 5:12. Eight years hence, 1/2 of A’s age at that time will be less than B’s age at that time by 2 years. What is B’s present age?

Let the present age of A be a years and that of B be b years
Then, 4 years ago,
A's age = (a - 4)
B's age = (b - 4)
Now, according to the given information in question,
{(a - b)/2}/4(b - 4) = 5/12 or (a - 4)/2(4b - 16) = 5/12 or (a - 4)/(4b - 16) = 5/6
By cross multiplying we get
or, 6a - 24 = 20b - 80
or, 6a - 20b = -56
or, 10b - 3a = 28
After 8 years,
(a + 8)2 + 2 = b + 8
or, a/2 + 4 + 2 = b + 8
or, b - a/2 = -2
or, 2b - a = -4 .......(i)
a = 2b + 4 ......(ii)
Putting the value of a in equation (i), we get
10b - 3(2b + 4) = 28
or, 4b = 40
∴ b = 10
Hence, the present age of B is 10 years.