Suzy is ten years older than Billy, and next year she will be twice as old as Billy. How old are they now?

Let the age of Suzy be S. It is given that she is 10 years older
than Billy. Let Billy be B years old. So S = B+10

Next year Suzy
will be S+1 years old and Billy will be B+1 years. Also, Suzy will be twice as old as Billy.
Therefore S+1 = 2(B+1)

=> S+1 = 2B +
2

=> B+ 10 +1 = 2B +2

=>
B+11 = 2B +2

=> B = 9.

So Billy
is 9 years old and Suzy is 9 +10 = 19 years old.

There
ages of Billy and Suzy now are 9 and 19 respectively.