Woman age is **24** and niece age is **8**.

**Solution:**

Six years ago a woman was nine times the age of her niece

f-6 = 9(n-6)

f-6 = 9n-54

f-9n = -54+6

f-9n = -48 .............(1)

she is now three times the age of her niece.

f = 3n; .................(2)

Then, add (2) in (1)

f-9n = -48

3n-9n = -48

-6n = -48

n = 48/6

n = 8

Hence, n = 8 is **niece** age.

And n = 8 add into (1)

f-9(8) = -48

f-72 = -48

f = -48+72

f = 24

Hence, f = 24 is **woman** age