I'm twice as old as you were, when i was old as you are. When you are as old as i am the sum of our ages will be 72. What is your age and my age?

lets assume that my age is x and your age is y, and x>y

I'm twice as old as you were, when i was old as you are.

this means that i was your age that is y years old before (x - y) years

before (x - y) years you were y - (x - y) years old

x = 2(y - (x - y))

When you are as old as i am the sum of our ages will be 72

you will have x years of age after x - y years

my age after x - y years will be x + (x - y)

x + (x - y) + y + (x - y) = 72

by solving the system of equations

x = 2(y - (x - y))

x + (x - y) + y + (x - y) = 72

we find

x = 32 years old

y = 24 years old

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i am 32 years old and you are 24 years old.