Question

Two numbers are in the ratio 2 : 3. When each of
the two numbers is increased by 8, the ratio between
them becomes 3 : 4. Find the two numbers.​

Answer 1

Answer:

2x+8/3x+8 = 3/4

(2x+8)4 = (3x+8)3

8x+32 = 9x+24

9x-8x = 32-24

x = 8

2x = 2x8 = 16

3x = 3X8 = 24

Answer 2

Given :

• Two numbers are in the ratio 2:3 .
• If both numbers are increased by 8 , the ratio becomes 3:4 .

To Find :

• Two numbers .

Solution :

$\longmapsto\tt{Let\:first\:number\:be=2x}$

$\longmapsto\tt{Let\:second\:number\:be=2x}$

Now ,

• If both numbers are increased by 8 , the ratio between them becomes 3:4 .

$\longmapsto\tt{First\:Number=2x+8}$

$\longmapsto\tt{Second\:Number=3x+8}$

A.T.Q :

$\longmapsto\tt{\dfrac{2x+8}{3x+8}=\dfrac{3}{4}}$

$\longmapsto\tt{4(2x+8)=3(3x+8)}$

$\longmapsto\tt{8x+32=9x+24}$

$\longmapsto\tt{8x-9x=24-32}$

$\longmapsto\tt{-x=-8}$

$\longmapsto\tt\bf{x=8}$

Value of x is 8 ..

Therefore :

$\longmapsto\tt{First\:Number=2(8)}$

$\longmapsto\tt\bf{16}$

$\longmapsto\tt{Second\:Number=3(8)}$

$\longmapsto\tt\bf{24}$

So , The Two numbers are 16 and 24 ..