Question

if twice the age of son is added to age of father the sum is 56 but if twice the age of father is added to the age of Son the sum is 82. find the ages of father and son.

Answer 1

let the age of son be X and father be y
equations => (1) 2x+y=56 (2) x+2y=82
elimination method
2x+y=56 X 2
x+2y=82 X 1
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4x+2y=112
(-)x+(-)2y=(-)82
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3x. =30
x=30/3=10
substitute x=10 in any one of these equations
2x+y=56
2(10)+y=56
20+y=56
y=56-20
y=36
therefore age of father is 36 and son is 10

Answer 2

Question:-

if twice the age of son is added to age of father the sum is 56 but if twice the age of father is added to the age of Son the sum is 82. find the ages of father and son.

Solution:-

Given:- a) twice the age of son is added to age of father the sum is 56 .

b) twice the age of father is added to the age of Son the sum is 82 .

Find:- The ages of father and son.

Let, age of son be x & age of father

be y .

{ From given ( a ) & ( b ) }

=> 2x + y = 56 ....... ( 1 )

=> 2y + x = 82 i.e.

=> x + 2y = 82 ........ ( 2 )

{ To find age of father }

multiply eq. ( 2 ) by 2

=> 2x + 4y = 164 ....... ( 3 )

substract eq. ( 3 ) from eq. ( 1 )

2x + y = 56

- ( 2x + 4y = 164 )

_______________

- 3y = - 108

3y = 108

y = 108/3

y = 36

{ To find age of son }

put value of y in eq. ( 1 )

=> 2x + y = 56

=> 2x + 36 = 56

=> 2x = 56 - 36

=> 2x = 20

=> x = 20/2

=> x = 10

Hence age of son & age of father is

10 { year's } & 36 { year's } respectively.

i hope it helps you