Question

Four years ago father was six timeas as old as his son. Ten years later, the father will be two and half times as old as his son. Determine the present age of father and son .​

Answer 1

Let the present age of the Son be : S

Let the present age of the Father be : F

Four Year's ago :

★  Age of father will be : (F - 4)

★  Age of father will be : (S - 4)

Given : Four year's ago, Father was six times as old as his son

$:\implies$  (F - 4) = 6(S - 4)

$:\implies$  F = 6S - 24 + 4

$:\implies$  F = 6S - 20

Ten year's later :

★  Age of father will be : (F + 10)

★  Age of father will be : (S + 10)

Given : 10 years later, Father will be two and half times as old as his son

$:\implies$  (F + 10) = 2.5(S + 10)

$:\implies$  F + 10 = 2.5S + 25

Substituting the value F = 6S - 20 in the above equation, We get :

$:\implies$  6S - 20 + 10 = 2.5S + 25

$:\implies$  6S - 10 = 2.5S + 25

$:\implies$  6S - 2.5S = 25 + 10

$:\implies$  3.5S = 35

$\mathsf{:\implies S = \dfrac{35}{3.5}}$

$:\implies$  S = 10

Substituting the value S = 10 in F = 6S - 20, We get :

$:\implies$  F = 6(10) - 20

$:\implies$  F = 60 - 20

$:\implies$  F = 40

Answers :

★  Present Age of Son = 10 years

★  Present Age of Father = 40 years