Question

Six years ago a woman was nine times the age of her niece and she is now three times the age of her niece.

What are their current ages?

Answer 1

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

Answer 2

Let X be current age of aunt and Y current age of niece
Then,
X - 6 = 9 x (Y - 6) (1)
X = 3 Y (2 )
By multiplying (2) by - 1 and adding both equations:
- 6 = 9Y - 54 - 3Y,
48 = 6Y ; Y = 8 and X = 3x8 = 24

Answer 3

CONSIDER THE PRESENT AGE OF WOMAN AND NIECE BE X and Y
THEN GET 2 EQUATIONS IE
X=3Y AND 9(Y-6)=X-6
SOLVING GET X=24 and Y=8 which is the answer