Question

Two numbers are in the ratio 5:9 if 3 is subtracted from each the ratio become 1:2 .find the numbers

Answer 1

let numbers be 5x, 9x

subtracting 3 from each we get 5x-3,9x-3

5x-3/9x-3 =1/2

2(5x-3)=9x-3

10x-6=9x-3

10x-9x= -3+6

x=3

5x= 5(3)=15

9x=9(3)=27

15,27 are numbers

Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• Two numbers are in the ratio 5:9

• If 3 is subtracted from each the ratio become 1:2

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• The numbers

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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Given that , the two numbers are in the ratio 5:9

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So,

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• Let the first number be "5x"

• Let the second number be "9x"

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$\underline{\bold{\texttt{First number :}}}$

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➠ 5x ⚊⚊⚊⚊ ⓵

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$\underline{\bold{\texttt{Second number :}}}$

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➠ 9x ⚊⚊⚊⚊ ⓶

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$\underline{\bold{\texttt{3 is subtracted from the first number :}}}$

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➜ 5x - 3 ⚊⚊⚊⚊ ⓷

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$\underline{\bold{\texttt{3 is subtracted from the second number :}}}$

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➜ 9x -3 ⚊⚊⚊⚊ ⓸

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Also given that , if 3 is subtracted from each the ratio become 1:2

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Thus ,

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From ⓷ & ⓸

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➜ $\sf \dfrac { 5x - 3 } { 9x - 3 } = \dfrac { 1 } { 2 }$

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➜ 2(5x - 3) = 9x - 3

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➜ 10x - 6 = 9x - 3

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➜ 10x - 9x = - 3 + 6

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➜ x = 3 ⚊⚊⚊⚊ ⓹

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⟮ Putting x = 3 from ⓹ to ⓵ ⟯

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➜ 5x

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➜ 5(3)

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➨ 15

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• Hence the 1st number is 15

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⟮ Putting x = 3 from ⓹ to ⓶ ⟯

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➜ 9x

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➜ 9(3)

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➨ 27

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• Hence the 2nd number is 27

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∴ The two numbers are 15 & 27