In fourteen years time, a mother will be as twice as her old son. Four years ago the sum of their ages was 30 years. Find how old the mother was, when the son was born ?

Let the current age of the son be x years and the current age of the mother be y years.

According to the given information:
In fourteen years time, the mother will be twice as old as her son:
y + 14 = 2(x + 14)

Four years ago, the sum of their ages was 30 years:
(x - 4) + (y - 4) = 30
x + y - 8 = 30
x + y = 38

Now, we can substitute the value of x + y from the second equation into the first equation:
38 - 8 = 30
y = 30 - 30
y = 8

Now, we can substitute the value of y into the first equation to find the age of the mother:
y + 14 = 2(x + 14)
8 + 14 = 2(x + 14)
22 = 2(x + 14)
11 = x + 14
x = 11 - 14
x = -3

Since the age of the son cannot be negative, there seems to be a mistake in the initial assumptions. Let's correct it.

Let the current age of the son be x years and the current age of the mother be y years.

According to the given information:
In fourteen years time, the mother will be twice as old as her son:
y + 14 = 2(x + 14)

Four years ago, the sum of their ages was 30 years:
(x - 4) + (y - 4) = 30
x + y - 8 = 30
x + y = 38

Now, we can substitute the value of x + y from the second equation into the first equation:
38 - 8 = 30
y = 30 - 30
y = 8

Now, we can substitute the value of y into the first equation to find the age of the mother:
y + 14 = 2(x + 14)
8 + 14 = 2(x + 14)
22 = 2(x + 14)
11 = x + 14
x = 11 - 14
x = -3

Since the age of the son cannot be negative, there seems to be a mistake in the initial assumptions. Let's correct it. Let's assume that the son is older than the mother.

Let the current age of the son be x years and the current age of the mother be y years.

According to the given information:
In fourteen years time, the mother will be twice as old as her son:
y + 14 = 2(x + 14)
y + 14 = 2x + 28
y = 2x + 14

Four years ago, the sum of their ages was 30 years:
(x - 4) + (y - 4) = 30
x + y - 8 = 30
x + y = 38

Now, we can substitute the value of y from the first equation into the second equation:
x + 2x + 14 = 38
3x + 14 = 38
3x = 24
x = 8

Now, we can substitute the value of x back into the first equation to find the age of the mother:
y = 2(8) + 14
y = 16 + 14
y = 30

So, the current age of the mother is 30 years and the current age of the son is 8 years.

When the son was born, the mother was:
30 - 8 = 22 years old.

Therefore, the mother was 22 years old when the son was born.