Question

the sum of the numerator and denominator of a given fraction is 12.If 3 is added to its denominator,then the fraction becomes 1\2. Find the given fraction.

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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

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• Sum of numerator and denominator is 12

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• Fraction becomes 1/2 when 3 is added to the denominator.

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$\red{\underline \bold{To \: Find:}}$

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Let the numerator be 'x'

Let the denominator be 'y'

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$\purple{\underline \bold{According \: to \: the \ question :}}$

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$\purple\longrightarrow$ $\sf x + y = 12$

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$\bf \dashrightarrow x = 12 - y$ ------(1)

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Also,

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$\sf \longmapsto \dfrac { x } { y + 3 } = \dfrac { 1 } { 2 }$-------(2)

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$\underline{\bold{\texttt{Putting value of x in (2)}}}$

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$\sf \longmapsto \dfrac { 12 - y} { y + 3 } = \dfrac { 1 } { 2 }$

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$\sf \longmapsto y + 3 = 24 - 2y$

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$\sf \longmapsto 3y = 21$

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$\sf \longmapsto y = \dfrac { 21 } { 3 }$

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$\bf\longmapsto y = 7$ ------(3)

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$\underline{\bold{\texttt{Putting y = 7 in (1)}}}$

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$\sf \longmapsto x = 12 - 7$

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$\bf\longmapsto x = 5$

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Hence numerator is 5 and denominator is 7

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$\underline{\bold{\texttt{Fraction is :}}}$

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$\bf \dashrightarrow \dfrac { 5 } { 7 }$

$\rule{200}5$