Question

The ratio of two numbers is 5:6. If each number is increased by 8, the ratio becomes 6:7 Find the numbers?​

Answer 1

Given :

• The ratio of two numbers is 5:6.
• If each number is increased by 8, the ratio becomes 6:7 .

To Find :

• Two numbers .

Solution :

$\longmapsto\tt{Let\:first\:number\:be=5x}$

$\longmapsto\tt{Let\:second\:number\:be=6x}$

Now ,

• If each number is increased by 8, the ratio becomes 6:7 .

$\longmapsto\tt{First\:Number=5x+8}$

$\longmapsto\tt{Second\:Number=6x+8}$

A.T.Q :

$\longmapsto\tt{\dfrac{5x+8}{6x+8}=\dfrac{6}{7}}$

$\longmapsto\tt{7(5x+8)=6(6x+8)}$

$\longmapsto\tt{35x+56=36x+48}$

$\longmapsto\tt{35x-36x=48-56}$

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

$\purple\longmapsto\:\large\underline{\boxed{\bf\blue{x}\pink{=}\red{8}}}$

Therefore :

$\longmapsto\tt{First\:Number=5(8)}$

$\longmapsto\tt\bf{40}$

$\longmapsto\tt{Second\:Number=6(8)}$

$\longmapsto\tt\bf{48}$

So , The two numbers are 40 and 48 .

Answer 2

Given that:

• The ratio of two numbers is 5 : 6.

To Find:

• The numbers.

Let us assume:

• First number be 5x.
• Second number be 6x.

Each number is increased by 8.

• First number = 5x + 8
• Second number = 6x + 8

Now, the ratio becomes 6 : 7.

According to the question.

ㅤ↠ㅤ(5x + 8) : (6x + 8) = 6 : 7

ㅤ↠ㅤ(5x + 8)/(6x + 8) = 6/7

Cross multiplication.

ㅤ↠ㅤ7(5x + 8) = 6(6x + 8)

ㅤ↠ㅤ35x + 56 = 36x + 48

ㅤ↠ㅤ36x + 48 = 35x + 56

ㅤ↠ㅤ36x - 35x = 56 - 48

ㅤ↠ㅤx = 8

Hence,

• First number = 5x = 5(8) = 40
• Second number = 6x = 6(8) = 48