Question

The denominator of a rational number is less than its numerator than 5.If 5 is added to the numerator,
the new number becomes 11/6.Find the original rational number​

Answer 1

$\large \bf \clubs \:  Given :-$

• The Denominator of a Rational Number is 5 less than the Numerator.

• If 5 is added to numerator , then it becomes 11/6.

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$\large \bf \clubs \:  To \: Find :-$

• The Original Rational Number.

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$\large \bf \clubs \:  Solution :-$

Let Numerator and Denominator of Original Rational Number be :

• Numerator = x

Accordingly :

• Denominator should be = x - 5

So ,

$\sf Original \: Number \: is :  \mathtt{\dfrac{x}{ x - 5} }$

When 5 is added to the Numerator :

$\sf Number \: Becomes : \mathtt{ \dfrac{x + 5}{x - 5} }$

According To Question :

$\mathtt{ \dfrac{x +5}{x - 5} } = \frac{11}{6} \\ \\ \large : \longmapsto \mathtt{6(x + 5) = 11(x - 5) } \\ \\ \large : \longmapsto \mathtt{6x + 30 = 11x - 55 } \\ \\ \large : \longmapsto \mathtt{5x = 85} \\ \\ \large :\longmapsto \tt x = \cancel\frac{85}{5} \\ \\ \Large\purple{ :\longmapsto \underline {\boxed{{\bf x = 17} }}}$

Hence,

$\sf Original\: Number\: is : {\dfrac{17}{ 17 - 5}}$

That Is :

$\underline\pink{\maltese \:\:\underline{\mathfrak{Original\:Rational \:Number=\dfrac{17}{12}}}}$

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

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Answer 2

Answer :

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• Original rational number is 17/12.

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Explanation :

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Given :

$\:$

• Denominator of a rational number is 5 less than it's numerator.

• If 5 is added to the numerator, the rational number becomes 11/6.

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To Find :

$\:$

• Original rational number?

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Solution :

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• Let the numerator of a rational number be n. It is stated in question that denominator of a rational number is 5 less than it's numerator. So, it's denominator is (n - 5).

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$\clubsuit$ According to the Question :

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• If 5 is added to the numerator, the rational number becomes 11/6.

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Therefore,

$\\ :\implies\:\sf \dfrac{n + 5}{n - 5} = \dfrac{11}{6}$

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By cross multiplying :

$\\ :\implies\:\sf 6\big(n + 5\big) = 11\big(n - 5\big)$

$\\ :\implies\:\sf 6n + 30 = 11n - 55$

$\\ :\implies\:\sf 11n - 6n = 30 + 55$

$\\ :\implies\:\sf 5n = 85$

$\\ :\implies\:\sf n = {\cancel{\dfrac{85}{5}}}$

$\\ :\implies\:\underline{\boxed{\bf{\purple{n = 17}}}}\:\bigstar$

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Hence,

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• Numerator = n = 17

• Denominator = (n - 5) = 17 - 5 = 12

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• Therefore, original rational number is 17/12.

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$\clubsuit$ Verification :

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➥ $\sf \dfrac{n + 5}{n - 5} = \dfrac{11}{6}$

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Putting value of 'n' in above eqⁿ :

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➥ $\sf \dfrac{17 + 5}{17 - 5} = \dfrac{11}{6}$

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➥ $\sf {\cancel{\dfrac{22}{12}}} = \dfrac{11}{6}$

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➥ $\underline{\boxed{\bf{\red{\dfrac{11}{6} = \dfrac{11}{6}}}}}\:\bigstar$

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$\therefore\:\underline{\textsf{\textbf{Hence,\:Verified}}}!$

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$\clubsuit$ Learn more on brainly :

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Question :

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In a fraction if one is added to both numerator and dinominator it becomes 1/2. if 1 is subtracted from both numerator and dinominator it become 1/3. find the fraction.

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Answer :

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https://brainly.in/question/41620598

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