Then the age difference between father and brother is X=A-B, and the age difference between brother and sister is Y = B-C.

A+B+C=64

My sister was nine years old when my father was three times older than my brother.

Then A'=(3/2)* X and B'=( 1/2)* X and C'=9.

When my brother is twice as old as my sister, my father is 34 years old.

Then a "= 34, b" = 2 * y and c "= y.

Because the age difference is constant.

So there is

①(3/2)* X-( 1/2)* X=34-2 * Y

②( 1/2)* X-9=2 * Y-Y

③(3/2)* X-9=34-Y

Obtained by ① ② ③ solution

X=26、Y=4

And because X=A-B, Y=B-C, A+B+C=64.

The solution is A=40, B= 14 and C= 10.

A: Now my father is 40 years old, my brother 14 years old and my sister 10 years old.