two years ago a woman was 7 times old as her daughter, but in 3 years time she would be 4 times old as the girl. how old are they now

Let present age of women be x.

Then,Present age of her daughter be y.

According to the question,

Two years ago,

Woman age = x - 2

Her daughter age = y - 2

Woman was 7 times old as her daughter. [ Given ]

x - 2 = 7 ( y - 2 )

=> x - 2 = 7y - 14

=> x - 2 + 14 = 7y

=> x + 12 = 7y ( i )

After Three years ,

Woman age = x + 3

Her daughter age = y + 3

she would be 4 times old as the girl. [ Given ]

x + 3 = 4 ( y + 3 )

=> x + 3 = 4y + 12

=> x = 4y + 12 - 3

=> x = 4y + 9( ii (

Now,

★ Putting the value of x = 4y + 9 from equation ( ii ) in equation ( i ),we get

x + 12 = 7y

=> 4y + 9 + 12 = 7y

=> 21 = 7y - 4y

=> 21 = 3y

=> 3y = 21

=> y = 21/3

=> y = 7

And,

x = 4y + 9

★ Putting the value of y in equation ( ii ), we get

x = 4 × 7 + 9

x = 28 + 9

x = 37

Hence, the present age of women is 37 years and her daughter age is 7.