Question

a father and his son decided 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:

Before Six Years,

Let's Son's age is X

So, Father's Age Should Be 5X

After Six Years ,

The Son's Age Become X+6 (1)

The Father's Age Become 5X+6 (2)

The Sum there Ages = 60 (Given)

(X+6)+(5X+6) = 60 (By Equation (1)&(2))

X+6+5X+6 = 60

6X+12= 60

6X = 60-12

6X = 48

X = 8 Years

So, The Son's in present = X+6 (1)

So, The Son's in present = X+6 (1)= 8+6 = 14

So, The Son's in present = X+6 (1)= 8+6 = 14So, six years from now the son's age will be = 14+6 =20

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 :

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

$\longmapsto\tt{14+6}$

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