Question

A father is 30 years older than his son, however, he will be only thrice as old as the son after 5 years. What is the father's present age ?

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Answer 1

Answer:

Step-by-step explanation:

Given,

• A father is 30 years older than his son however he will be only thrice as old as the son after 5 years.

To Find,

• Present age of the father.

Solution,

Let the present age son be x years.

And the present age of father be y years.

Here,

y = x + 30 .. (i)

After 5 years,

Son's age = (x + 5) years.

Father's age = (y + 5) years.

According to the question,

⇒ 3(x + 5) = (y + 5)

⇒ 3x + 15 = y + 5

⇒ 3x + 15 = x + 30 + 5

⇒ 3x + 15 = x + 35

⇒ 3x - x = 35 - 15

⇒ 2x = 20

⇒ x = 20/2

⇒ x = 10 years.

Here, the son's present age is 10 years.

Now, the present age of the father,

Putting x's value in eq (i), we get

⇒ y = x + 30

⇒ y = 10 + 30

⇒ y = 40 years.

Hence, the father's present age is 40 years.

Answer 2

Answer:

Given :-

• A father is 30 years older than his son, however, he will be only thrice as old as the son after 5 years.

To Find :-

• What is the father's present age.

Solution :-

Let,

$\mapsto \bf{Present\: age\: of\: son\: =\: x\: years}$

$\mapsto \bf{Present\: age\: of\: father =\: (x + 30)\: years}$

After 5 years :

$\leadsto$ Present age of son = (x + 5) years

$\leadsto$ Present age of father :

$\leadsto \sf x + 30 + 5\: years$

$\leadsto \sf\bold{\green{x + 35\: years}}$

According to the question,

$\implies \sf 3(x + 5) =\: x + 35$

$\implies \sf 3x + 15 =\: x + 35$

$\implies \sf 3x - x =\: 35 - 15$

$\implies \sf 2x =\: 20$

$\implies \sf x =\: \dfrac{20}{2}$

$\implies \sf \bold{\purple{x =\: 10\: years}}$

Hence, the required present ages are :

➲ Present age of son :

$\longrightarrow \sf Present\: Age_{(Son)} =\: x\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Son)} =\: 10\: years}}$

➲ Present age of father :

$\longrightarrow \sf Present\: Age_{(Father)} =\: (x + 30)\: years$

$\longrightarrow \sf Present\: Age_{(Father)} =\: (10 + 30)\: years$

$\longrightarrow \sf\bold{\red{Present \: Age_{(Father)} =\: 40\: years}}$

${\small{\bold{\underline{\therefore\: The\: present\: age\: of\: father\: is\: 40\: years\: .}}}}$