Question

A father is now three times as old as his son.
Five years back, he was four times as old as
his son. The age of the son in years) is:
(A) 10
(B) 12
(C) 15
(D) 18​

Answer 1

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• A father is now three times as old as his son.

• Five years back, he was four times as old as his son.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The present age of son.

$\bf{\underline{\underline\green{Solution:-}}}$

According to the 1st condition:-

A father is now three times as old as his son.

Let the present age of son be x

Present age of father = 3x

According the the 2nd condition:-

Five years back, he was four times as old as his son.

Five years ago:-

Age of son = Present age - 5

Age of son = x - 5

Age of father = Present age - 5

Age of father = 3x - 5

Father is four times as old as his son.

So:-

$\sf \implies 3x - 5 = 4(x - 5)$

$\sf \implies 3x - 5 = 4x - 20$

$\sf \implies 3x -4x = - 20 + 5$

$\sf \implies - x = - 15$

$\sf \implies \cancel- x = \cancel- 15$

$\sf \implies x = 15$

The present age of son = x = 15

The present age of father

= 3x

= 3 × 15

= 45

The present age of father = 45

$\underline{ \boxed { \purple{\sf \therefore The \: present \: age \: of \: son= 15 \: years}}}$

$\rm Option \: (C) \: is \: correct$

Answer 2

Given:

Father is three times old as his son.

So,

Let the age of son be x years and

So the age of the father will be 3x years

Now,

According to the question:

Five years back, he was four times as old as his son,

Thus,

⇒ 3x - 5 = 4(x - 5)

⇒ 3x - 5 = 4x - 20

⇒ 20 - 5 = 4x - 3x

[By transporting (-20) to LHS and (3x) to RHS]

⇒ 15 = x

Therefore

The present age of the son is x years = 15 years.

So,

The correct option will be (C) 15

- - -

We can get the age of the father (present) = 3x = 3*15 = 45 years old.

Five years back his age will be (3x - 5) = 45 - 5 = 40 years old.

Five years back his son age will be (x-5) = 15 - 5 = 10 years old.

Now,

If we check their age according to the question we can verify their age

Five years back he was four times old as his son,

Son = 4(x - 5) = 4*10 = 40

Father = (3x - 5) = 45 - 5 = 40

Both RHS and LHS are equal.

Hence

Verified.