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