These Timelines Are So Confusing

Let your age be $x$ , and your mother's age be $y$ .

Seven years ago, my mother was seven times older than me:

$y-7 = 7(x-7) \implies$ Eq. (1)

In exactly eight years from now, my mother will be two times older than me:

$y+8=2(x+8) \implies$ Eq. (2)

Now, we just need to solve the simultaneous equations:

From Eq. (1):

$y-7=7x-49$

$y=7x-42\implies$ Eq. (3)

Substitute Eq. (3) into Eq. (2):

$7x-42+8=2x+16\\ 5x=50\implies x=10$

Use this value to find your mother's age:

$y+8=2(10+8)\\ y=\boxed{28}$

Using logic, we can deduce the mother's age.

In the second line, 'In exactly eight years from now, my mother will be two times older than me.', we can deduce that the age must be an even number, because when 8 is added to the age the total must be divisible by 2.

This rules out 25 and 27.

The first line states that 'Seven years ago, my mother was seven times older than me.' This means that 7 years ago, the mother's age was divisible by 7.

$(26 - 7) mod7 = 5$

$(28 - 7) mod7 = 0$

Therefore the mother's age now is 28.