Question

A father and his son decides to sum their age. The sum is equal to sixty years. Six years ago the age of the father was five times the age of the son. Six years from now the son's age will be

Answer 1

Answer:

First, let's find out the father and son's age six years ago. To do this, we need to find out the sum of their ages six years ago. As 6 + 6 = 12, the sum of their ages six years ago will 60 - 12 = 48.

Let's keep the son's age as x.

The father's age is equal to 5x.

So, 48 = x + 5x.

x + 5x can also be written as 1x + 5x = 6x.

As 48 is equal to 6x, the value of 'x' will be 48 divided by 6 which is equal to 8. So, the son was 8 years old 6 years ago.

Now, to find the present age of the son, we have to do 8 + 6 = 14 years old. As the question asks us to find the son's age 6 years from now, we have to do 14 + 6 = 20 years old.

Therefore, the son after six years will be 20 years old.

Now that you have got your answer, here are all the results of the question:

• Son's current age = 14
• Father's current age = 46
• Son's age six years ago = 8
• Father's age six years ago = 40
• Son's age 6 years from now = 20
• Sum of their both ages currently = 60
• Sum of their both ages 6 years back = 48

Hope this helps you!

Answer 2

Given :

The sum of the ages of father and son is 60 yrs .

Six years ago the age of the father was five times the age of the son.

To Find :

Age of the son after 6 years .

Solution :

$\longmapsto\tt{Let\:the\:son's\:age\:be=x}$

$\longmapsto\tt{Let\:the\:father's\:age\:be=y}$

$\longmapsto\tt{x+y=60-------(1)}$

Before 6 years :

$\longmapsto\tt{Age\:of\:son=x-6}$

$\longmapsto\tt{Age\:of\:father=y-6}$

A.T.Q :

$\longmapsto\tt{y-6=5(x-6)}$

$\longmapsto\tt{y-6=5x-30}$

$\longmapsto\tt{y=5x-30+6}$

$\longmapsto\tt\bf{y=5x-24}$

Putting the value of y in eq. (1) :

$\longmapsto\tt{x+5x-24=60}$

$\longmapsto\tt{6x-24=60}$

$\longmapsto\tt{6x=60+24}$

$\longmapsto\tt{6x=84}$

$\longmapsto\tt{x=\cancel\dfrac{84}{6}}$

$\longmapsto\tt\bf{x=14}$

Therefore :

After 6 years :

$\longmapsto\tt{Age\:of\:son=x+6}$

$\longmapsto\tt{14+6}$

$\longmapsto\tt\bf{20\:yrs}$