# Mark is 4 years older than his sister. What are their ages if after 3 years Mark will be twice her age.

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Let mark's age be M and his sister's age is S

Given that mark is 4 years older than his sister:

Then M = S + 4 ............(1)

Now after 3 years:

Mark's age = M + 3

His sister's age = S + 3

But Mark's age will be twice his sister's age:

==> M+3 = 2 ( S+3)

==> M + 3 = 2S + 6

==> M = 2S + 3

But from (1) we know that M = S + 4

==> S + 4 = 2S + 3

==> S = 1

Then the sister's age = 1 year old

Then Mark is 1+ 4 = 5 years old Now

After 3 years:

Mark will be 5+3 = 8 years old

His sister's age will be 1 + 3 = 4 years old

We are given that Mark is 4 years older than his sister and after 3 years Mark will be twice her age.

Let Mark be M years old. So as he is 4 years older than his sister, his sister's age is M- 4.

After three years his age is M+3 and his sister's age will be M-4+3

Now M+3 = 2( M+ 3- 4)

=> M+ 3 = 2M -2

=> M = 5

**Therefore Mark is 5 years old and his sister is 1 year old.**