Question

A fraction becomes 4/5 when 5 is added to
its numerator and 1 is subtracted from its
denominator It becomes 1/2 when 3 and 5
are subtracted from its numerator and
denominator. The numerator of the
fraction will be​

Answer 1

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

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$\large{\green{\underline \bold{\tt{Given :-}}}}$

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• A fraction becomes 4/5 when 5 is added to its numerator and 1 is subtracted from its denominator

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• It becomes 1/2 when 3 and 5 are subtracted from its numerator and denominator

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$\large{\red{\underline \bold{\tt{To \: Find :-}}}}$

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• The numerator of the fraction

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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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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A fraction becomes 4/5 when 5 is added to its numerator and 1 is subtracted from its denominator

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➠ $\sf \dfrac { x + 5 } { y - 1 } = \dfrac { 4 } { 5 }$

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➜ 4y - 4 = 5x + 25

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➜ 4y - 5x = 29 -------- (1)

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Also given that , fraction becomes 1/2 when 3 and 5 are subtracted from its numerator and denominator

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

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➜ y - 5 = 2x - 6

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➜ y - 2x = -1 -------- (2)

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⟮ Multiplying equation (2) by 4 ⟯

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➜ 4y - 8x = -4 -------- (3)

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⟮ Subtracting equation (3) from (1) ⟯

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➜ 4y - 5x -(4y - 8x) = 29 - (-4)

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➜ 4y - 5x - 4y + 8x = 29 + 4

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➜ 3x = 33

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➨ x = 11

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• Hence the numerator of the fraction is 11

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⟮ Putting x = 11 in (2) ⟯

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➜ y - 2x = -1

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➜ y - 2(11) = -1

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➜ y - 22 = - 1

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➨ y = 21

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• Hence denominator is 21

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$\underline{\bold{\texttt{Original fraction :}}}$

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➼ $\bf \dfrac { 11 } { 21 }$

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Answer 2

$\large{\orange{\underline{\tt{Solution :-}}}}$

$\:\:$

Let the numerator be x

Let the denominator be y

$\:\:$

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

$\:\:$

A fraction becomes 4/5 when 5 is added to its numerator and 1 is subtracted from its denominator

$\:\:$

➠ $\sf \dfrac { x + 5 } { y - 1 } = \dfrac { 4 } { 5 }$

$\:\:$

➜ 4y - 4 = 5x + 25

$\:\:$

➜ 4y - 5x = 29 -------- (1)

$\:\:$

Also given that , fraction becomes 1/2 when 3 and 5 are subtracted from its numerator and denominator

$\:\:$

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

$\:\:$

➜ y - 5 = 2x - 6

$\:\:$

➜ y - 2x = -1 -------- (2)

$\:\:$

⟮ Multiplying equation (2) by 4 ⟯

$\:\:$

➜ 4y - 8x = -4 -------- (3)

$\:\:$

⟮ Subtracting equation (3) from (1) ⟯

$\:\:$

➜ 4y - 5x -(4y - 8x) = 29 - (-4)

$\:\:$

➜ 4y - 5x - 4y + 8x = 29 + 4

$\:\:$

➜ 3x = 33

$\:\:$

➨ x = 11

$\:\:$

Hence the numerator of the fraction is 11

$\:\:$

⟮ Putting x = 11 in (2) ⟯

$\:\:$

➜ y - 2x = -1

$\:\:$

➜ y - 2(11) = -1

$\:\:$

➜ y - 22 = - 1

$\:\:$

➨ y = 21

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Hence denominator is 21

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$\underline{\bold{\texttt{Original fraction :}}}$

$\:\:$

➼ $\bf \dfrac { 11 } { 21 }$

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