Question

The numerator of a fraction is 3 less than the denominator. If both the numerator and the denominator are increased by 2the new fraction becomes 6/7.find original fraction

Answer 1

Answer:

19/1

Step-by-step explanation:

Let the numerator be x-3 and denominator be x

X-3+2/x+2=6/7

x-1/x+2=6/7

7x-7=6x+12

X=16/1

Answer 2

Let,

$\mapsto \bf{Denominator =\: x}$

$\mapsto \bf{Numerator =\: x - 3}$

$\leadsto \sf \dfrac{Numerator}{Denominator}</p><p>\leadsto \sf\bold{\green{\dfrac{x - 3}{x}}}$

$\purple{\bigstar}\: \: \bf{According\: to\: the\: question\: :-}$

$\begin{gathered}\implies \sf \dfrac{Numerator + 2}{Denominator + 2} =\: New\: fraction\\\end{gathered} \\ \\ \implies \sf \dfrac{x - 3 + 2}{x + 2} =\: \dfrac{6}{7} \\ \\ \implies \sf \dfrac{x - 1}{x + 2} =\: \dfrac{6}{7}$

$\begin{gathered}\purple{\bigstar}\: \: \bf{By\: doing\: cross\: multiplication\: we\: get\: :-}\\\end{gathered}$

$\implies \sf 7(x - 1) =\: 6(x + 2) \\ \implies \sf 7x - 6x =\: 12 + 7 \\ \implies \sf\bold{\green{x =\: 19}}$

Hence, the required original fraction will be :

$\longrightarrow \sf Original\: Fraction =\: \dfrac{x - 3}{x}$

$\longrightarrow \sf Original\: Fraction =\:\dfrac{19 - 3}{19}$

$\longrightarrow \sf\bold{\red{Original\: Fraction =\: \dfrac{16}{19}}}$

${\small{\bold{\underline{\therefore\: The\: original\: fraction\: is\: \dfrac{16}{19}\: .}}}}$

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$\large \bold{@WildCat7083}$