20. The sum of the present ages of a mother and her
daughter is 60 years. When the mother attains her
husband's present age, the ratio of her husband's
age and her daughter's age would be 2 : 1. Find the
present ageſ of the daughter. (in years)
Answers
Let the present ages of Daughter be "D'', mother be "M" & husband be "H".
Given, D + M = 60....(i)
Let after 'x' years, mother attains the age of husband(daughter's father)
So after 'x' years:
Daughter's age = D + x
Mother's age = M + x = H (present age of husband or his age 'x' years back)
Husband's age = H + x
Also given, Husband's age : daughter's age = 2:1
(H+x)/(D+x) = 2/1
H + x = 2*(D + x)
H = 2*D + 2x-x = 2*D + x
H = 2D + x ......(ii)
We also had M+x = H
So, M + x = 2D + x
M = 2D ....(iii)
Substitute (iii) in (i)
(i)== M + D = 60
2D + D = 60
3D = 60
D = 20 years.
Hence present age of daughter is '20' years.
Hope this helps
Let the present ages of Daughter be "D'', mother be "M" & husband be "H".
Given, D + M = 60....(i)
Let after 'x' years, mother attains the age of husband(daughter's father)
So after 'x' years:
Daughter's age = D + x
Mother's age = M + x = H (present age of husband or his age 'x' years back)
Husband's age = H + x
Also given, Husband's age : daughter's age = 2:1
(H+x)/(D+x) = 2/1
H + x = 2*(D + x)
H = 2*D + 2x-x = 2*D + x
H = 2D + x ......(ii)
We also had M+x = H
So, M + x = 2D + x
M = 2D ....(iii)
Substitute (iii) in (i)
(i)== M + D = 60
2D + D = 60
3D = 60
D = 20 years.
Hence present age of daughter is '20' years.
Hope this helps