Question

08. In a fraction's numerator is increased by 1 and the denominator is increased by 2 then the fract
ion be comes 2/3. But when the numerator is increased by 5 and the denominator is increased by 1 then the fraction becomes 5/4. What is the value of the original fraction?*
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Answer 1

$\large \bf \clubs \:  Given :-$

• In a fraction's numerator is increased by 1 and the denominator is increased by 2 then the fraction be comes 2/3.

• When the numerator is increased by 5 and the denominator is increased by 1 then the fraction becomes 5/4.

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$\large \bf \clubs \:  To \: Find :-$

• The Original Fraction

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$\large \bf \clubs \:  Solution :-$

For Original Fraction Let,

• Numerator = x

• Denominator = y

So ,

$\text{Original Fraction} = \dfrac{ \text x}{ \text y}$

✏ When numerator is increased by 1 and the denominator is increased by 2 :

$\text{Fraction Becomes : } \dfrac{ \text x + 1}{ \text y + 2}$

According To Question :

$\dfrac{\text x + 1}{\text y + 2} = \dfrac{2}{3}$

$:\longmapsto3(\text x + 1) = 2(\text y + 2)$

$:\longmapsto3\text {x + 3 = 2y + 4}$

$:\longmapsto \bf{3x - 2y = 1} \: \: - - - (1)$

✏ When the numerator is increased by 5 and the denominator is increased by 1 :

$\text{Fraction Becomes : } \dfrac{ \text x + 5}{ \text y + 1}$

According To Question :

$\dfrac{\text x + 5}{\text y + 1} = \dfrac{5}{4}$

$:\longmapsto\text{4(x + 5) = 5(y + 1)}$

$:\longmapsto\text{4x + 20 = 5y + 5}$

$:\longmapsto \bf4x - 5 y = - 15 \: - - - (2)$

✏ Solving (1) and (2) :

$\purple{ \large :\longmapsto  \underline {\boxed{{\bf x = 5 \: \: and \: \:y = 7 } }}}$

Hence ,

$\large \underline{ \pink{ \underline{ \pmb{ \frak {Original \: Fraction = \dfrac{5}{7} } }}}}$

$\Large\red{\mathfrak{  \text{W}hich \:\:is\:\: the\:\: required} }\\ \LARGE \red{\mathfrak{ \text{ A}nswer.}}$

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Answer 2

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