Past, Present, Future

Let it be 'y' years ago. ATQ: His age=x yrs

Brothers age=x/2 yrs

Hence y years later ;

His age=x+y yrs.

Brothers age=x/2 + y ------(1)

Given that his age today is 8x, so x+y=8x

Y=7x-------(2)

Substitute (2) in (1) to get brothers age as

15(x)/2--------(3)

It is also given that a year later his age will be 33.

x+y+1=33

8x=32 {from (2)}

X=4

Substitute this in (3) to get brothers age as 30.

Since my age next year is $33$ , my age now is $32$ . If my age now is $8$ times my age in an unspecified year long ago, my age in that year would be $4$ and at the same time my younger brother's age would be $2$ since his age was half of my age in that time. With all of this said, we can now know our age gap is $2$ years.

A lot of people would think that my younger brother's age would still be half my age, making his age to be $16$ . But that's not the case. Now that we've established that our ages are $2$ years apart, my younger brother's age this year is $\boxed{30}$ , not $16$ since that would make our age gap become $16$ years which would change our original age gap.