Question

Mother is three times as old as her daughter. Three years ago she was four times as old as her daughter was. Find their present ages.​

Answer 1

daughter = 9yrs

mother = 27yrs

Explanation:

let age of daughter be x

age of mother = 3x

by qsn,

three yrs ago,

4 (x-3) = 3x-3

4x-12 = 3x-3

4x-3x = -3+12

× = 9 yrs (age of daughter )

3x = 3×9 = 27 yrs ( age of mother)

Answer 2

Let m represent the mother’s age and d represent the daughter’s age

m = 3d…(1)

(m-3) = 4(d-3), or
m - 3 = 4d - 12
m = 4d - 12 + 3
m = 4d - 9

m = 4d-9 …(2)

Substitute (1) into (2)

3d = 4d - 9
-d = -9
d = 9

Find the mother’s age by substituting d=9 into equation 1:
m=3d
m=3(9)
m=27

Therefore, the mother is 27 years and the daughter is 9 years old now