Question

two numbers are in the ratio 3 : 5 if 8 is added to each number the ratio becomes 2 : 3 find the numbers

Answer 1

let 3x, 5x are numbers
add 8
3x+8:5x+8
ratio=2:3
3x+8/5x+8 =2/3
3(3x+8) =2(5x+8)
9x+24=10x+16
10x-9x=24-16
x=8
3x=3(8)=24
5x=5(8)=40
24,40 are numbers

Answer 2

let the nos be 3x and 5x

now ATP

if 8 is added to each number the ratio becomes 2 : 3    

the nos become 3x + 8  and 5x + 8

Now [3x + 8]  / [5x + 8] =2 / 3

⇒3* [3x + 8]  =  [5x + 8] *2

⇒9x +24 = 10x + 16

⇒24 - 16 = 10x - 9x

⇒8 = x

the numbers are

⇒3x =3 * 8 =24     ANS

and  5x = 5 * 8 = 40 ANS

hope this will be helpful to u