Question

Two numbers are in the ratio 3 : 7. If 6 be added to each of them, then they are in the ratio 5 : 9. Find the numbers.​

Answer 1

⧠ Let the numbers be 3x and 7x.

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$\bigstar\:\boldsymbol{\underline{According\;to\;the\;problem}}$

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$\implies\sf{\cfrac{3x+6}{7x+6}=\cfrac{5}{9}}\\\\\\\implies\sf{5(7x+6)=9(3x+6)}\\\\\\\implies\sf{35x+30=27x+54}\\\\\\\implies\sf{35x-27x=54-30}\\\\\\\implies\sf{8x=24}\\\\\\\implies\sf{x=\dfrac{\cancel{24}}{\cancel{\:8\:}}}\\\\\\\implies{\underline{\boxed{\pink{\frak{x=3}}}}}{\:\bigstar}$

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Therefore,

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• First number = 3x = 3 × 3 = 9
• Second number = 7x = 7 × 3 = 21

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$\sf{Hence,\;the\;two\;numbers\;are\;{\bf{9}}\;and\;{\bf{21}}}.$

Answer 2

${\pmb {\sf {Question :}}}$

Two numbers are in ratio 3:7 .If 6 be added to each of them, then they are in ratio 5:9.Find the numbers.

${\pmb {\sf {Solution :}}}$

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Let the number be 3x and 7x respectively ⠀

$\bigstar\:\boldsymbol{\underline{According\;to\;the\; question }}$

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$\begin{gathered}\implies\sf{\cfrac{3x+6}{7x+6}=\cfrac{5}{9}}\\\\\\\implies\sf{5(7x+6)=9(3x+6)}\\\\\\\implies\sf{35x+30=27x+54}\\\\\\\implies\sf{35x-27x=54-30}\\\\\\\implies\sf{8x=24}\\\\\\\implies\sf{x=\dfrac{\cancel{24}}{\cancel{\:8\:}}}\\\\\\\implies{\underline{\boxed{\green{\sf{x=3}}}}}\end{gathered}$

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Therefore,

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First number = 3x = 3 × 3 = 9

Second number = 7x = 7 × 3 = 21

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$\sf{Hence,\;the\;two\;numbers\;are\;{\bf{9}}\; and \; {\bf {21}}}$