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.
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At presentDaughter'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
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