Question

Father’s age is 4 times his son’s age. After 5 years, father will be 3 times as old as his son. Find their present ages.

Answer 1

Answer :-

• The present age of the son = 10 years.

• The present age of the father = 40 years.

Given :-

• A father's age is 4 times his son's age.

• After 5 years, the father will be 3 times as old as his son.

To find :-

• Their present ages.

Step-by-step explanation :-

• Let the present age of the son be x.

• Then the father's age will be 4x.

After 5 years,

• The age of the son will be x + 5.

• The age of the father = 4x + 5.

• It has been given that after 5 years, the father will be 3 times as old as his son.

After five years,

• Three times the son's age = 3 (x + 5)

Therefore,

$\sf\implies 4x + 5 = 3 \: (x + 5)$

Removing the brackets,

$\sf\implies 4x + 5 = 3x + 15$

Transposing 5 from LHS to RHS, changing it's sign,

$\sf \implies 4x = 3x + 15 - 5$

Subtracting 5 from 15,

$\sf \implies 4x = 3x + 10$

Transposing 3x from RHS to LHS, changing it's sign,

$\sf\implies 4x - 3x = 10$

Subtracting 3x from 4x,

$\underline{ \boxed{ \implies \sf x = 10.}}$

• The value of x is 10.

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Therefore, their present ages are as follows :-

$\tt Son's \: age = x = 10.$

$\tt Father's \: age = 4x = 4 \times 10 = 40.$

Answer 2

Given :

• Father’s age is 4 times his son’s age.
• After 5 years, father will be 3 times as old as his son.

To Find :

• Their Present Ages

Solution :

⟼ Let the Present age of Son be x

⟼ Then Father's age will be 4x

✰ After 5 years :

⟼ The Present age of Son will be x + 5

⟼ Then Father's age will be 4x + 5

According to the Question :

⟹ Father's age = 3 × Son's age

⟹ 4x + 5 = 3 (x + 5)

⟹ 4x + 5 = 3x + 15

⟹ 4x - 3x = 15 - 5

⟹ x = 10

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Therefore :

• Father's Age = 4x = 4(10) = 40years
• Son's age = x = 10years

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