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.



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Answer 1

given: the ratio of the numbers is 2:3

let the numbers be 2x and 3x respectively

when increased by 8, ratio becomes 3:4

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

cross multiply

8x+32=9x+24

32-24=9x-8x

8=x

so the numbers are:-

2x is 2*8=16

3x is 3*8= 24

Answer 2

Given :

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

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

A.T.Q :

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

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

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

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

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

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

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 ..