Ex.2.6 Q7 Linear Equations in One Variable Solutions-Ncert Maths Class 8

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Question

The denominator of a rational number is greater than its numerator by \(8\). If the numerator is increased by \(17 \) and the denominator is decreased by \(1\), the number obtained is \(\begin{align}\frac{3}{2}\end{align}\).Find the rational number.

Text Solution

What is known?

i) The denominator of a rational number is greater than its numerator by \(8\)

ii) If the numerator is increased by \(17\) and the denominator is decreased by 1, the number obtained is \(\begin{align}\frac{3}{2}\end{align}\)

What is unknown?

the rational number

Reasoning:

Assume numerator of the fraction as variable. Use first condition to express denominator in the form of variable and use second condition to form the equation.

Steps:

Let the numerator of the rational number be \(x\) Therefore, its denominator will be \(x + 8\).

The rational number will be\(\begin{align}\frac{x}{{x + 8}}\end{align}\). According to the question,

\[\begin{align}\,\,\frac{{x + 17}}{{x + 8 - 1}} &= \frac{3}{2} \\\,\,\,\,\,\,\frac{{x + 17}}{{x + 7}} &= \frac{3}{2} \\2\left( {x + 17} \right) &= 3\left( {x + 7} \right) \\\,\,\,2x + 34 &= 3x + 21 \\\,\,\,34 - 21 &= 3x - 2x \\\,\,\,\,\,\,\,\,\,\,\,\,\,13 &= x \\\end{align}\]

Numerator of the rational number \(= x = 13\)

Denominator of the rational number \(= x + 8 = 13 + 8 = 21\)

Rational number \(=\begin{align} \frac{{13}}{{21}}\end{align}\)

  
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