Question

5 years ago, a mother was 7 times as old as her daughter.5 years hence, she will be 3 times as old as her daughter. Fine their present ages.

Answer 1

At present
Daughter's age = x years
Mother age =y
5 years ago
Daughter's age =x-5
Mother's age = y-5
Mother's age=7*daughter's age
y-5=7(x-5)
y-5=7x-35
7x-y=30----(1)
After 5 years
Mother's age =y+5
Daughter's age =x+5
Mother's age=3*Daughter's age
y+5=3(x+5)
y+5=3x+15
3x-y=-10----(2)
Subtract (2) from (1)
4x=40
x =40/4
x=10
Substitute x=10 in (2)
3*10-y= -10
30-y =-10
-y =-10-30
y =40
At present
Daughter's age =x =10 years
Mother's age =y=40years

Answer 2

Let the present age of daughter be x.

5 years ago,

Her age is x-5.

Her mother's age is 7(x-5).

Including 5 years from past to present and then to future=10

ATQ

7x-35+10=3(x-5+10)

7x-25=3x+15

7x-3x=25+15

4x=40

x=10

So daughter age= 10

Mother's age=4×10=40