Question

The age of father 10 years ago was thrice the age of his son. Ten years hence, fathers ' age will be twice that of his son's age. Find the ratio of their present ages.

Answer 1

Answer:

Let the age of Father and son be x and 3x years respectively.

After Ten years,

Age of father = x + 10 years

Age of son = 3x + 10

According to Question now,

(3x + 10) + 10 = 2(x + 10) + 10

3x + 20 = 2(x + 20)

3x + 20 = 2x + 40

3x - 2x = 40 - 20

x = 20 years.

Therefore, Required ratio :

(3x + 10) : (x + 10)

3(20) + 10 : 20 + 10

60 + 10 : 30

70 : 30

7 : 3

Therefore, the required ratio is 7:3.

Answer 2

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Let the present age of father and son be x and y years respectively.

10 years ago

Father's age was (x-10) years and son's age was (y-10) years

Acc to ques.

(x-10)=3(y-10)

x-10=3y-30

x-3y=-20 (1)eq

After 5 years,

Age of father will be (x+10) years and that of son will be (y+10) years

Again, (x+10)=2(y+10)

x+10=2y+20

x-2y=10 (2)eq

Solving equations 1 and 2

y=30 and x= 70

Thus ratio of father and son's age is 70:30

Or, 7:3