Question

13. A man is four times as old as his son. After 20 years, he will be twice as old as his
son at that time. Find their present ages.
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Answer 1

Answer:

let present age of son is x

Father's age = 4x

after 20 years

son's age = x + 20

father's age = 2(x + 20)

x + 20 = 2x + 40

x = 20

Answer 2

Given:-

• A man is four times as old as his son.
• After twenty years, he will be as old as his son at that time.

To Find:-

• Their present ages.

Solution:-

Let the age of son be x

Age of man = 4x

Now,

After 20 years,

Age of Son = x + 20

Age of man = 4x + 20

ATQ,

After 20 years man will be twice of his son.

Hence,

2(x + 20) = 4x + 20

= 2x + 40 = 4x + 20

= 2x - 4x = 20 - 40

= -2x = -20

⇒ x = -20/-2

⇒ x = 10

Putting the value of x in the ages of man and son we assumed:-

• Age of son = x = 10
• Age of man = 4x = 4 × 10 = 40

Therefore,

• Age of son is 10 years
• Age of man is 40 years

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Verification:-

Let's see after 20 years will the age of man be twice of his son or not.

After 20 years

• Age of son = 10 + 20 = 30 years
• Age of man = 40 + 20 = 60 years

Dividing age of man by his son,

= 60/30 = 2

Hence, yes the age of man becomes twice of his son after 20 years.

Hence Verified!!!

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