Question

The denominator of a rational number is greater than its Numerator by 3.If 3 is subtracted from the numerator and 2 is added to its denominator.The new number becomes 1 5 .Find the original Rational numbers.

Answer 1

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• The denominator of a rational number is greater than its numerator by 3 if 3 is subtracted from the numerator and 2 is added to its denominator the new number becomes 1 / 5 find the original number.

$\star{ \underline{ \underline{ \frak{ \Large{ \pink{Answer: - }}}}}}$

$\sf \: Let, the \: numerator \: of \: rational \: number \: x$

Then,

$\sf \: Denominator = x + 3$

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$\star{ \sf{ \underline{According \: to \: the \: question,}}}$

$:\implies \sf \: \: \: \frac{x - 3}{x + 3 + 2} = \frac{1}{5} \\ \\ \\ :\implies \sf \: \: \: \frac{x - 3}{x + 5} = \frac{1}{5} \\ \\ \\ :\implies \sf\: \: \:5x - 15 = x + 5 \\ \\ \\ :\implies \sf\: \: \: 5x - x = 5 + 15 \\ \\ \\ :\implies \sf \: \: \: 4x = 20 \\ \\ \\ :\implies \sf \: \: \: x = \cancel\frac{20}{4} \\ \\ \\ :\implies \sf \: \: \: { \sf{ \red{ \boxed{x = 5}}}}$

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$\sf \: The \: original \: rational \: fraction \: is : - \\ \\ \sf\longmapsto \frac{5}{5 + 3} \\ \\ \sf \longmapsto { \blue{ \boxed{\frac{5}{8} }}}$

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Answer 2

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• The denominator of a rational number is greater than its numerator by 3 if 3 is subtracted from the numerator and 2 is added to its denominator the new number becomes 1 / 5 find the original number.

$\sf{\huge{\bold{\pink{\bigstar{\boxed{\boxed{Solution}}}}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• numerator = x
• denominator = x + 3

$\sf{\bold{\blue{\underline{\underline{To\:Find}}}}}$

• The original fraction

$\sf{\bold{\purple{\underline{\underline{Solution}}}}}$

$\sf\dfrac{x - 3}{x + 3 + 2} = \dfrac{1}{5}$

$\sf\dfrac{x-3}{x+5} = \dfrac{1}{5}$

• cross multiplication

$\sf 5 {x - 3} = x + 5$

$\sf 5x - 15 = x + 5$

$\sf 5x - x = 15 + 5$

$\sf 4x = 20$

$\sf x = \dfrac {\cancel{20}}{\cancel{4}}$

$\sf x = 5$

• required fraction

$\dfrac{x}{x + 3} = \dfrac{5}{5+3}$

$\dfrac{5}{8}$

$\sf{\bold{\red{\boxed{\dag \dfrac{5}{8}}}}}$

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