Question

pls urgent 6 years ago, a man's age was six times the age of his daughter. After 4 years, thrice his age will be equal to eight times his daughter's age. What are their present ages? Find it.

Answer 1

Answer:

Let the present age of man be x years and that of his daughter be y years.

x - 6 = 6(y - 6)

x - 6 = 6y - 36

x - 6y = -36+6

x - 6y = -30    (1)

3(x + 4) = 8(y + 4)

3x + 12 = 8y + 32

3x - 8y = 32 - 12

3x - 8y = 20    (2)

Multiplying eq (1) by 3 we get,

3(x - 6y) = 3(-30)

3x - 18y = -90    ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(3)

Subtracting (2) from (3) we get,

3x - 18y = -90

+3x - 8y = 20

-     +         -

___________

        -10y = -110

             y = 11

Substituting the value of y in eq (1) we get,

x - 6(11) = -30

x - 66 = -30

x = -30 + 66

x = 36

Hence, the present age of father is 36 years and that of his daughter is 11 years.