Math, asked by GaanaOriginals, 3 months ago

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.​

Answers

Answered by wtfhrshu
67

⧠ 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}}}.

Answered by IamJaat
111

  {\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}}}

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