Question

Two numbers are in the ratio of 2:3 . If 15 added to both the number,then the ratio between two number become 11/14. Find the greater number

Answer 1

Given :

• Two numbers are in the ratio of 2:3 .
• If 15 added to both the number , then the ratio between the two numbers become 11/14.

To Find :

• Greater number .

Solution :

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

$\longmapsto\tt{Let\:second\:number\:be=3x}$

Now ,

• If 15 added to both the number , then the ratio between the two numbers become 11/14.

$\longmapsto\tt{First\:Number=2x+15}$

$\longmapsto\tt{First\:Number=3x+15}$

A.T.Q :

$\longmapsto\tt{\dfrac{2x+15}{3x+15}=\dfrac{11}{14}}$

$\longmapsto\tt{14(2x+15)=11(3x+15)}$

$\longmapsto\tt{28x+210=33x+165}$

$\longmapsto\tt{28x-33x=165-210}$

$\longmapsto\tt{-5x=-45}$

$\longmapsto\tt{x=\cancel\dfrac{-45}{-5}}$

$\longmapsto\tt\bf{x=9}$

Value of x is 9 .

Therefore :

$\longmapsto\tt{First\:Number=2(9)}$

$\longmapsto\tt\bf{18}$

$\longmapsto\tt{Second\:Number=3(9)}$

$\longmapsto\tt\bf{27}$

So , The Second number (27) is greater than the first number (18) .

Answer 2

Answer:

Given:

• Two numbers are in the ratio of 2:3 . If 15 added to both the number,then the ratio between two number become 11/14. Find the greater number

To find:

• The greater one?

Solution:

Let the first no. be 2x

Let the second no. be 3x

•°•First no. = 2x + 15

•°•First no. = 3x + 15

According to the Question,

$\sf{ \mapsto \frac{2x + 15}{3x + 15} = \frac{11}{14} }$

$\sf{ \mapsto14(2x + 15) = 11(3x + 15)}$

$\sf{ \mapsto28x + 210 = 33x + 165}$

$\sf{ \mapsto28x - 33x = 165 - 210}$

$\sf{ \mapsto \: x = \frac{ - 45}{ - 5} = 9 }$

$\bold{ \longmapsto \: x = 9}$

Therefore,

The First no. be

$\bold\mapsto{ \pink{2(9) = 18}}$

The Second no be.

$\bold \mapsto{ \pink{3(9) = 27}}$

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