The ratio of the present ages of a mother and daughter is 7:1 . Four years ago the ratio of their ages was 19:1 . What will be the mother's age four years from now?

Method 1
Let us assume the present age of mother be M and daughter be D.
According to question,
Ratio of present age of mother and daughter = 7 : 1
M / D = 7 : 1
? M / D = 7 / 1
? M / D = 7
? M = 7D ..........................(1)
Four years ago the age of mother = M - 4
Four years ago the age of daughter = D - 4
Again according to question,
Four years ago ratio of mother age and daughter age = 19 : 1
? (M - 4 ) / (D - 4) = 19 : 1
? (M - 4 ) / (D - 4) = 19
? (M - 4 ) = 19(D - 4)
? M - 4 = 19D - 76 .....................(2)
Put the value of M from equation (1) in above equation (2), we will get
7D - 4 = 19D - 76
? 76 - 4 = 19D - 7D
? 72 = 12D
? 12D = 72
? D = 72/12
? D = 6
Put the vale of D in equation (1), we will get the present age of mother.
Present age of Mother M = 7D = 7 x 6
Present age of Mother M = 42
? mother's age after 4 yrs = 42 + 4 = 46 yrs

Method 2
Let us assume the ratio factor is x.
According to question,
Ratio of present age of mother and daughter = 7 : 1
Then present age of mother = 7x and present age of daughter = x
Four years ago the age of mother = 7x - 4
Four years ago the age of daughter = x - 4
Again according to question,
Four years ago ratio of mother age and daughter age = 19 : 1
? (7x - 4 ) / (x - 4) = 19 : 1
? (7x - 4 ) / (x - 4) = 19
? (7x - 4 ) = 19(x - 4)
? 7x - 4 = 19x - 76
? 76 - 4 = 19x - 7x
? 72 = 12x
? 12x = 72
? x = 6
Present age of Mother = 7x = 7 x 6 = 42
? mother's age after 4 yrs = 42 + 4 = 46 yrs