Question

Two numbers are in the ratio 3:5. When 8 is added to each, the ratio changes
to 5:7. Identify the two numbers
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Answer 1

Given :

• Two numbers are in the ratio 3:5. When 8 is added to each, the ratio changes
• to 5:7.

To Find :

• The Numbers

Solution :

➞ Let the first number be 3x

➞ Let the second number be 5x

After adding 8 :

➞ The first number = 3x + 8

➞ The second number = 5x + 8

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According to the Question :

⠀⠀⟼⠀⠀3x + 8/5x + 8 = 5/7

⠀⠀⟼⠀⠀7(3x + 8) = 5(5x + 8)

⠀⠀⟼⠀⠀21x + 56 = 25x + 40

⠀⠀⟼⠀⠀56 - 40 = 25x - 21x

⠀⠀⟼⠀⠀16 = 25x - 21x

⠀⠀⟼⠀⠀16 = 4x

⠀⠀⟼⠀⠀16/4 = x

⠀⠀⟼⠀⠀4 = x

⠀

Therefore :

➥ First Number = 3x

➥ First Number = 3 × 4

➥ First Number = 12

⠀

➥ Second Number = 5x

➥ Second Number = 5 × 4

➥ Second Number = 20

⠀

Thus the Number are 12 and 20

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Answer 2

Given :

• Two numbers are in the ratio 3:5. When 8 is added to each, the ratio changes to 5:7

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To find :

• The two numbers.

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Solution :

• As in the question it is given That if 3:5 is added to the Number 8. So we will let the numbers be 3y and 5y. Firstly we will add (3y + 8)/(5x + 8) and their sum is 5/7. Then we will find the value of y and after finding the value of y. We will get the required numbers.

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$\color {red}\star \:$Let 1st Number be = 3y + 8

$\color {red}\star \:$2nd Number be = 5y + 8

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According to Question :

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$~~~~~~~~~$$:{ \implies \tt \dfrac{3y + 8}{5y + 8} = \dfrac{5}{7} }$

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$~~~~~~~~~$$:\implies \tt7 (3y + 8) = 5(5x + 8)$

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$~~~~~~~~~$$:\implies \tt21y + 56 = 25y + 40$

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$~~~~~~~~~$$:\implies \tt56 - 40 = 25y - 21y$

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$~~~~~~~~~$$:\implies \tt16 = 4y$

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$~~~~~~~~~$$:\implies \tt y = \dfrac{16}{4} \:$

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$~~~~~~~~~$$:\implies \tt{y = 4 }$

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${ \bf{First \: Number = 3x}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = { \bf{\:3\times 4}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \bf{ = 12}}$

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${ \bf{Second \: Number = 5}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = { \bf{\:5\times 4}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \bf{ = 20}}$

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${\underline{\boxed{ \frak{\color{blue} { \therefore{The \: Numbers \: are \: 12 \: and \: 20}}}}}}$

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