Question

36. The denominator of a rational number greater than its numerator by 8. If the numbrator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number











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Answer 1

Answer:

Let the numerator of the rational number be x.

So as per the given condition, the denominator will be x + 8.

The rational number will be x/x + 8.

According to the given cndition,

x + 17/x + 8 – 1 = 3/2

=x + 17/x + 7 = 3/2

=2(x + 17) = 3(x + 7)

=2x + 34 = 3x + 21

=34 − 21 = 3x − 2x

=x=13

Numerator of the rational number = x = 13

Denominator of the rational number = x + 8 = 13 + 8 = 21

Rational number = 13/21

Explanation:

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Answer 2

Answer :

Let the numerator of the rational number be $\sf\green{x}$

So as per the given condition, the denominator will be $\sf\green{</strong><strong>x\</strong><strong>:</strong><strong> </strong><strong>+</strong><strong> </strong><strong>\</strong><strong>:</strong><strong> </strong><strong>8</strong><strong>}$

$\sf\red{The\: rational \: number \: will\: be \: x/x \: +\: 8.}$

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$\begin{gathered}\begin{gathered}\underline{\boldsymbol{According\: to \:the\: Question :}} \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:x\: +\: \frac{17}{x} \: + \: 8 \: - \: 1 = \: \frac{3}{2} }} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\ : \implies \displaystyle \sf \: x \: + \: \frac{17}{x} \: + \: 7 \: = \: \frac{3}{2} \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\ : \implies \displaystyle \sf \: 2(x + 17) \: =\: 3(x + 7)\\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\ : \implies \displaystyle \sf \: 2x\: +\: 34\: =\: 3x\: + \: 21\\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\\ : \implies \displaystyle \sf \: 34\: − \: 21 \: = \: 3x\: −\: 2x \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\:x\: =\: 13 }} }\\ \\\end{gathered}\end{gathered}$

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Numerator of the rational number = x = 13

Denominator of the rational number = x + 8 = 13 + 8 = 21

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$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold {\: Rational \: number \: = \: \frac{13}{21} }} }\\ \\\end{gathered}\end{gathered}$