Suzy is ten years older than Billy, and next year she will be twice as old as Billy. How old are they now?
Let Suzy's age be S
Let Billy's age be B
==> given that Suzy's 10 years older that Billy:
==> S = B + 10 ..............(1)
Next year :
Suzy's age will be S + 1
Billy Will be B+1
But given that Suzy will be twice Billy's age:
==> S+1 = 2 ( B+1)
==> S + 1= 2B + 2
==> S = 2B + 1
But from (1) we know that S = 10 + B
==> 10 + B = 2B + 1
==> B = 9
==> S = 19
Then Billy's age= 9
And Suzy's age = 19
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.