Question

If twice the age of son is added to age of
father the sum is 63. But if twice the age
of father is added to the age of son, the
sum is 87. Find the ages of father and son
respectively.​

Answer 1

Answer:

Let the age of son = x yrs. and father's age = y yrs.

ATQ

Case I :

2x + y = 63                        

⇒ y = 63 - 2y           ..........(1)

Case II :

2y + x = 87

Substitute value of y from eq. 1

⇒ 2 ( 63 - 2x ) + x = 87

⇒ 126 - 4x + x = 87

⇒ 126 - 3x = 87

⇒ - 3x = 87 - 126

⇒ - 3x = - 39

⇒  3x = 39

⇒ x = 39 / 3

⇒ x = 13

y = 63 - 2x

⇒ y = 63 - 2 ( 13 )

⇒ y = 63 - 26

⇒ y = 37

∴ Father's age = 37 yrs

Son's age = 13 yrs

Answer 2

Let the son's age and the father's age be x and y respectively.

Given

Twice the age of son + The father's age = 63

$\implies 2x + y = 63$

Twice the father's age + Son's age = 87

$\implies 2y+x=87$

Equations obtained are:

$2x+y=63--(1)\\2y+x=87--(2)$

Multiplying the first equation by 2, we get,

$4x+2y=126\\\underline{x+2y=87}\\\underline{\underline{3x = 39}}\\\implies x = 13$

$13+2y=87\\\implies 2y= 87-13\\\implies 2y = 74\\\implies y = 37$

$\boxed{\boxed{\bold{Therefore, \ the \ father's \ and \ the \ son's \ age \ are \ 37 \ and \ 13 \ respectively }}}}}}$