Question

The sum of the ages of a father and his son is 55 years. After 16 years the father will be
twice as old as the son. What are their present ages.(Ans.: 42yrs., 13yrs.)​

Answer 1

Answer:

42yrs, 13yrs

let the age of son be x

father's age = 55-x

..

after 16 years their ages will be:

son x+16

father 55-x+16= 71-x

..

Father's age = twice son's age

 

71-x= 2(x+16)

71-x = 2x +32

3x= 71-32

3x=39

x=13 years, son's age

Father's age = 55-x

= 55-13

=42 years

Please mark it as the brainliest

Answer 2

Step-by-step explanation:

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

• The sum of the ages of a father and his son is 55 years.

• After 16 years the father will be
• twice as old as the son.

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

• The present ages of Father and his son.

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

Let the present age of father be x

As, the sum of ages of Father and his son is 55

The present age of son = 55 - x

After 16 years:-

Age of father = x + 16

Age of son = 55 - x + 16 = 71 - x

Given, the father will be twice as old as the son.

$\rm \implies x + 16 = 2( 71- x)$

$\rm \implies x + 16 = 142 - 2x$

$\rm \implies x + 2x = 142 - 16$

$\rm \implies 3x = 126$

$\rm \implies x = \dfrac{126}{3}$

$\rm \implies x = 42$

The present age of father = x = 42

The present age of son

= 55 - x

= 55 - 42

= 13

The present age of son = 13

$\underline{\boxed{\pink{\rm The \: present\: age\: of\: son = 13\: years}}}$

$\underline{\boxed{\purple{\rm The \: present\: age\: of\: father = 42\: years}}}$