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Five years ago, father was 4 times as old as his son and five years hence, he will be 2 times as old as his son will be. Find their present ages. Also find the ratio of the ages of father and son when father’s age is 60 years.
1. 35, 20; 3 ∶ 4
2. 25, 10; 4 ∶ 3
3. 45, 20; 7 ∶ 5
4. 35, 10; 6 ∶ 5

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Correct Answer - Option 2 : 25, 10; 4 ∶ 3

Given

Before 5 years’ father was 4 times as old as his son.

After 5 years father will be 2 times as old as his son.

Formula Used

Concept of Linear Equations, Elimination Method.

Calculation

Let father’s present age be ‘x’ years and son’s present age be ‘y’ years.

Five years’ ago,

Father’s age = (x – 5) years

Son’s age = (y – 5) years

So, (x – 5) = 4(y – 5)

⇒ x – 4y = - 15      ----(1)

Five years later, father’s age = (x + 5) years and son’s age = (y + 5) years

So, (x + 5) = 2(y + 5)

⇒ x – 2y = 5 (2)

Subtracting eq. (2) from (1), we get

-2y = -20

⇒ y = 10

put y = 10 in eq (1)

x – 4(10) = - 15

⇒ x = 40 – 15

⇒ x = 25

After 35 years father’s age will be 60 years = 25 + 35 = 60 years

So, Son’s age after 35 years = 10 + 35 = 45 years

Hence, Ratio of their ages when father’s age will be 60 years = 60/45 = 4 ∶ 3

∴ Father’s present age is 25 years and Son’s age is 10 years and the required ratio is 4 ∶ 3.

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