Math, asked by prakashu6567, 7 hours ago

The denominator of a fractions is 4 more than twice the numerator. When both numerator anddenominator are decreased by 6, then the denominator becomes 12 times the numerator. Findthe fraction.

Answers

Answered by Anonymous
64

Step-by-step explanation:

 \tt \underline{ \pink{Given:}}

The denominator of a fractions is 4 more than twice the numerator. When both numerator and denominator are decreased by 6, then the denominator becomes 12 times he numerator.

  \tt \underline{ \pink{To \:  Find}}

The fraction

 \tt{ \underline{ \pink{Solution:}}}

 \pink{ \tt{ Let}}

  • Numerator be x
  • Denominator=2x+4

  \sf \:  \N ew \:numerator = x - 6 \\   \sf\N ew \: denominator = 2x + 4 - 6 = 2x - 2

Now denominator has become 12 times the numerator. So, if we multiply 12 to the numerator after decreasing 6 from it, it will be equal to the denominator after decreasing 6 from it.

 \tt \: \red{ ACQ}

 \therefore \tt \: 12(x - 6) = 2x - 2 \\ \tt \leadsto12x - 70 = 2x - 2 \\ \tt \leadsto \: 12x - 2x =  - 2 + 72 \\ \tt \leadsto10x = 70 \\ \tt \leadsto \: x =  \frac{ \cancel{70}}{ \cancel{10} } \\  \green{\underline{ \tt \: x = 7}}

Now, numerator=x=7

Denominator=2x+4=2×7+4=14+4=18

 \blue{ \tt \: Required \: fraction =  \frac{7}{18} }

Answered by mddilshad11ab
181

\sf\small\underline{Let:-}

\tt{\leadsto The\: numerator\:_{(fraction)}=x}

\tt{\leadsto The\:denominator\:_{(fraction)}=y}

\tt{\leadsto The\: Fraction=\dfrac{x}{y}}

\sf\small\underline{To\: Find:-}

\tt{\leadsto The\: Fraction\:_{(number)}=?}

\sf\small\underline{Solution:-}

To solve this question at 1st we have to set equation then calculate the Numerator and denominator. After that substituting the value of Numerator and denominator to calculate the fractional number.

\sf\small\underline{Given\:in\:case-(i):-}

\rm{\implies Denominator=2(Numerator)+4}

\rm{\longrightarrow y=2x+4}

\rm{\longrightarrow 2x-y=-4-----(i)}

\sf\small\underline{Given\:in\:case-(ii):-}

\rm{\implies Denominator-6=12(Numerator-6)}

\rm{\longrightarrow y-6=12(x-6)}

\rm{\longrightarrow 12x-y=66----(ii)}

  • In eq (i) × by 12 and eq (ii) × by 2:-

\rm{\longrightarrow 24x-12y=-48}

\rm{\longrightarrow 24x-2y=132}

  • By Solving we get here :-

\rm{\longrightarrow -10y=-180}

\rm{\longrightarrow 10y=180}

\rm{\longrightarrow y=18}

  • Putting the value y= 18 in eq (i):-

\rm{\longrightarrow 2x-y=-4}

\rm{\longrightarrow 2x-18=-4}

\rm{\longrightarrow 2x=-4+18}

\rm{\longrightarrow x=7}

\sf\small\underline{Hence,\:the\: fraction=\frac{7}{18}}

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