Question

the denominator of a rational number is greater than its numerator by 4. if 3 subtracted from the numerator and 4 added to the denominator, the new number becomes 2/13. find the original number

pls tell me the ans of this :(

Answer 1

$\\ \underline\red{\rm \large{Answer :- }}$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \implies \: \dfrac{25}{29}$

$\\ \underline\red{\rm \large{Solution :- }}$

Let the numerator be x .

So, the denominator of rational number is greater than its numerator by 4.

Then denominator be (4+x)

Now, According to the question

$\\ \sf \: \: \: \: \: \: \: \: \implies \: \dfrac{(x - 3)}{(4 + x) + 4} = \dfrac{2}{3}$

$\\ \sf \: \: \: \: \: \: \: \: \implies \: \dfrac{(x - 3)}{(8+ x) } = \dfrac{2}{3}$

$\\ \sf \: \: \: \: \: \: \: \: \implies \:3 {(x - 3)} = 2{(8+ x)}$

$\\ \sf \: \: \: \: \: \: \: \: \implies \:3x - 9= 16+ 2x$

$\\ \sf \: \: \: \: \: \: \: \: \implies \:3x - 2x= 16+ 9$

$\\ \sf \: \: \: \: \: \: \: \: \implies \: x= 16+ 9$

$\\ \sf \: \: \: \: \: \: \: \: \implies \boxed{ \pink{\frak{\: x= 25}}}$

Now , We know that

$\\ \sf \: \: \: \: \: Numerator \: = x \: = 25$

$\\ \sf \: \: \: \: \: Denominator = 4 + x \\ \: \sf \: \: \: \: \: \:\: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4 + 25 \\ \: \sf \: \: \: \: \:\: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: \: \: = \underline\pink{29}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \green{ \sf \: \: \: So, \: The \: fraction \: is \: \: \dfrac{25}{29} .}$

Answer 2

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GiveN :-

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• The denominator of a rational number is greater than its numerator by 4. If 3 subtracted from the numerator and 4 added to the denominator, the new number becomes 2/13

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To FinD :-

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• The original number.

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SolutioN :-

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Let the numerator be x and denominator be 4+x

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$\qquad \quad : \implies \sf\dfrac{(x - 3)}{(4 + x) + 4} = \dfrac{2}{13}$

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$\qquad \qquad : \implies \sf{ \dfrac{(x - 3)}{(8 + x)} = \dfrac{2}{13} }$

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$\quad \quad : \implies \sf{13(x - 3) = 2(8 + x)}$

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$\qquad \quad : \implies \sf{13x - 39 = 16 + 2x}$

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$\qquad \quad : \implies \sf{13x - 2x = 16 + 39}$

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$\quad \qquad : \implies \sf{11x = 55}$

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$\qquad \qquad : \implies \sf{x = \dfrac{ 55}{11} }$

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$\qquad \qquad : \implies \sf{x = 5}$

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We also know that :-

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$\qquad \quad \begin{gathered}{ \boxed{ \underline{ \bf{ \red{Numerator = x = 5}}}}} \end{gathered}$

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$\qquad \qquad \begin {gathered}{ \boxed{ \underline{ \bf{ \red{Denominator = 4 + x = 4 + 5 = 9}}}}} \end{gathered}$

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$\begin{gathered}{ \boxed{ \underbrace{ \sf{ \blue{Therefore, \: the \: fraction \: is \: \frac{5}{9} }}}}} \end{gathered}$

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