Math, asked by amitkumar10012003, 5 months ago

The ratio of two numbers is 3:5. if both numbers are increased by 5, their ratio becomes 2:3. find the number​

Answers

Answered by sethrollins13
133

Given :

  • Two numbers are in the ratio 3:5 .
  • If both are increased by 5 , the ratio becomes 2:3 .

To Find :

  • The numbers .

Solution :

\longmapsto\tt{Let\:First\:Number\:be=3x}

\longmapsto\tt{Let\:Second\:Number\:be=5x}

Now ,

  • If both are increased by 5 , the ratio becomes 2:3 .

\longmapsto\tt{First\:Number=3x+5}

\longmapsto\tt{Second\:Number=5x+5}

A.T.Q :

\longmapsto\tt{\dfrac{3x+5}{5x+5}=\dfrac{2}{3}}

\longmapsto\tt{3(3x+5)=2(5x+5)}

\longmapsto\tt{9x+15=10x+10}

\longmapsto\tt{9x-10x=10-15}

\longmapsto\tt{-1x=-5}

\longmapsto\tt{x=5}

Value of x is 5 .

Therefore :

\longmapsto\tt{First\:Number=3(5)}

\longmapsto\tt\bf{15}

\longmapsto\tt{Second\:Number=5(5)}

\longmapsto\tt\bf{25}

So , The two numbers are 15 and 25 .

Answered by Clαrissα
75

Given :

  • The ratio of two numbers is 3:5. if both numbers are increased by 5, their ratio becomes 2:3.

To Find :

  • The numbers ?

Solution :

Put x in the ratio

Numbers = 3x , 5x

Increased by 5,

  • 3x + 5
  • 5x + 5

According to question :

➙ 3x + 5/5x + 5 = 2/3

➙ 3 (3x + 5) = 2 (5x + 5)

➙ 9x + 15 = 10x + 10

➙ 10x - 9x = 15 - 10

➙ x = 5

Put the value of x in the ratio

  • 3x = 3 × 5 = 15
  • 5x = 5 × 5 = 25

Hence, the numbers are 15 and 25 respectively.

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