Question

son age is one-third that of his father. Five years ago father age was 4 times as old as his son. Find their present age​

Answer 1

To find their present ages we will first let the father's age be x. Then, son's age will be x/3. Five years ago son's age will be (x/3 - 5) and father's age will be (x - 5). It is given father's age was 4 times son's age.
(X-5)=4(X/3-5)
=x-5=(4x-60/3)
=3(x-5)=4x-60
=3x-15=4x-60
=3x-4x=-60+15
=-1x=-45
X=45
The fathers age is 45
The son’s age is 10

Answer 2

Step-by-step explanation:

Hello user,

Given that

• Son's age is ⅓ that of his father.

• Five years ago, father's age was 4 times his son's age.

To find:

• What are their present ages?

Process:

To find their present ages we will first let the father's age be x. Then, son's age will be x/3. Five years ago son's age will be (x/3 - 5) and father's age will be (x - 5). It is given father's age was 4 times son's age. So, we can form an equation as follows:

• x - 5 = 4(x/3 - 5)

After solving the equation to get the value of x, the value of x is equal to the age of the father and x/3 will be the age of the son.

Solution:

Let the father's age be x.

Then, the son's age will be x/3.

Five years ago:

Son's age = (x/3 - 5)

Father's age = (x - 5)

∵ Five years ago father's age was 4 times his son's age. [given]

$∴ \tt \red {x−5=4 \bigg( \frac{x}{3} −5 \bigg)}$

$⟹ \tt \red{x - 5 = \frac{4x}{3} - 20}$

$⟹ \tt \red{x - \frac{4x}{3} = 5 - 20}$

$⟹ \tt \red{\frac{3x - 4x}{3} = - 15}$

$⟹ \tt \red{\frac{ - x}{3} = - 15}$

$⟹ \tt \red{- x = - 15 \times 3}$

$⟹ \tt \red{ \cancel- x = \cancel- 45}$

$⟹ \tt \red{x = 45}$

Hence, value of x is 45.

Therefore, father's age = x = 45 years

And son's age = x/3 = 45/3 = 15 years.