Math, asked by shreyassshete9822, 4 months ago

The sum of the numerator and the denominator of a fraction is 12. If the denominator is increased
by 3, the fraction becomes
 \frac{1}{2}
. Find the fraction.​

Answers

Answered by ShírIey
186

❍ Let the Numerator of the fraction be x and the Denominator of the fraction be y respectively.

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\qquad\quad\boxed{\bf{\mid{\overline{\underline{\bigstar\: According\: to \; the\; Question \: :}}}}\mid}\\\\

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  • The sum of the numerator and the denominator of a fraction is 12.

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Therefore,

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:\implies\sf x + y = 12 \\\\\\:\implies\sf x = 12 - y \qquad\quad\bigg\lgroup\bf Equation\; (i) \bigg\rgroup

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  • If the denominator is increased by 3, the fraction becomes ½.

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Therefore,

:\implies\sf \dfrac{Numerator}{Denominator} = \dfrac{x}{y} \\\\\\:\implies\sf \dfrac{x}{y + 3} = \dfrac{1}{2} \\\\\\:\implies\sf  2x = y + 3 \qquad\quad\bigg\lgroup\bf Equation \;(II)\bigg\rgroup

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\underline{\bf{\dag} \:\mathfrak{Putting\; value\; of\; x \; in\; equation (2)\: :}}

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:\implies\sf 2(12 - y) = y + 3\\\\\\:\implies\sf 24 - 2y = y + 3\\\\\\:\implies\sf   3y = 21\\\\\\:\implies\sf y = \cancel\dfrac{21}{3}\\\\\\:\implies{\underline{\boxed{\frak{\pink{y = 7}}}}}\;\bigstar

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\underline{\bf{\dag} \:\mathfrak{Putting\; value\; of \; y \: in\; equation (1)\: :}}⠀⠀

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:\implies\sf x = 12 - y\\\\\\:\implies\sf x = 12 - 7\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 5}}}}}\;\bigstar

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Hence,

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  • Numerator of the fraction, x = 5

  • Denominator of the fraction, y = 7

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\therefore{\underline{\sf{Hence, \; the \: fraction\; is\; \bf{ \dfrac{5}{7}}.}}}

Answered by BrainlyCyclone
56

Answer:

 \large \sf \pink{Given}

  • Sum of numerator and denominator = 12
  • If the denominator is increased by 3, the fraction becomes ½

 \large \sf \red{To \: Find}

Denominator and Numerator

 \large \sf \blue{Solution}

Let the fraction be x/y

Hence,

x + y = 12

x/y + 3 = ½

Now,

 \sf \: x = 12 - y \bigg \lgroup equation \: 1 \bigg \rgroup

 \sf \: 2x = y + 3 \bigg \lgroup \: equation \: 2 \bigg \rgroup

2(12 - y) = y + 3

(2 × 12) - (2 × y) = y + 3

24 - 2y = y - 3

24 - 3 = 2y + y

21 = 2y + y

21 = 3y

y = 21/3

y = 7

 \large \bf \green{Denominator = 7}

Now

x + y = 12

x + 7 = 12

x = 12 - 7

x = 5

 \large \bf \green{Numerator = 5}

 \large \bigstar \large \sf \pink{Fraction =  \dfrac{5}{7}}

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