Question

linear equation. ten years later A will be twice as old as B and ten years ago A was twelve times as old as B. What ate the present ages of A and B

Answer 1

let present age of a and b be x and y
linear equation
x+10=2 (y+10)
x-10=12 (y-10).
on solving x is 34 and y is 12

Answer 2

let x be the present age of A and y be the present age B
question says , ten year later

Age of A ( x + 10 )
Age of B (y +10)

A/q , A. = 2 B

=> (x+10 ) = 2( y+10)
=> x + 10 = 2y + 20
=> x - 2y = 10
=> x = 10 +2y ...1)

Second condition
10 year ago
Age of A (x - 10)
and Age of B (y- 10)

A/q , A = 12B

=> ( x-10 ) = 12 ( y- 10)
=> x -10 = 12 y - 120
=> x - 12y = -120+10
=> x - 12y = -110 ....2)

putting 1) in 2)

10 + 2y - 12y = -110

=> - 10 y = -110-10
=> 10 y = 120
=> y = 12

and x= 10 +2y => 10 +2×12

=> 10 + 24 => 34
x = 34

hence y = 10 and x = 34