5. The denominator of a rational number is greater than its numerator by 10. If the numerator is increased by 19 and the denominator is decreased by 1, the number obtained is ³/2. Find the rational number.

5. The denominator of a rational number is greater than its numerator

1.	5. The denominator of a rational number is greater than its numerator by 10. If the numerator is increased by 19 and the denominator is decreased by 1, the number obtained is ³/2. Find the rational number.
Answer» <html><body><h3><u><a href="https://interviewquestions.tuteehub.com/tag/correct-409949" style="font-weight:bold;" target="_blank" title="Click to know more about CORRECT">CORRECT</a></u><u> Question</u> :-</h3><p>The denominator of a rational number is greater than its numerator by 10. If the numerator is increased by 19 and the denominator is <a href="https://interviewquestions.tuteehub.com/tag/decreased-7266469" style="font-weight:bold;" target="_blank" title="Click to know more about DECREASED">DECREASED</a> by 1, the number <a href="https://interviewquestions.tuteehub.com/tag/obtained-7273275" style="font-weight:bold;" target="_blank" title="Click to know more about OBTAINED">OBTAINED</a> is 3/2. Find the rational number.</p><p></p><h2><u>Answer</u><u>:</u><u>-</u></h2><p>The required rational number is <strong>1</strong><strong>1</strong><strong>/</strong><strong>2</strong><strong>1</strong>.</p><p></p><h3>Step-by-step explanation</h3><p><strong>To </strong><strong>Find</strong><strong> </strong><strong>:</strong><strong>-</strong></p><ul><li>The rational number.</li></ul><p></p><p>★ <strong>S</strong><strong>o</strong><strong>l</strong><strong>u</strong><strong>t</strong><strong>i</strong><strong>o</strong><strong>n</strong></p><p>Given that,</p><p>The denominator of a rational number is <strong>greater</strong> than it's numerator by <strong>1</strong><strong>0</strong>.</p><p></p><p><u>Assumption</u> </p><p>Let us assume the <strong>numerator</strong><strong> </strong>& <strong>denominator</strong> as <strong>(</strong><strong>x)</strong><strong> </strong>and <strong>(</strong><strong>x </strong><strong>+</strong><strong> </strong><strong>1</strong><strong>0</strong><strong>)</strong><strong> </strong>respectively.</p><p></p><p><u>Also given</u>,</p><p>The <strong>numerator</strong> is increased by <strong>1</strong><strong>9</strong><strong> </strong>and the <strong>denominator</strong> is decreased by <strong>1</strong>. The <a href="https://interviewquestions.tuteehub.com/tag/new-1114486" style="font-weight:bold;" target="_blank" title="Click to know more about NEW">NEW</a> rational number is <strong>3</strong><strong>/</strong><strong>2</strong>.</p><p></p><p><u>According</u><u> the</u><u> question</u>, </p><p>Numerator = (x) + 19 = (x + 19)</p><p>Denominator = (x + 10) - 1 = (x + 9).</p><p></p><h3>∴ (x + 19)/(x + 9) = 3/2</h3><p></p><p>By simplifying,</p><p><strong>⇒</strong> (x + 19)/(x + 9) = 3/2</p><p><strong>⇒</strong> 3(x + 9) = 2(x + 19)</p><p><strong>⇒</strong> 3x + 27 = 2x + 38</p><p><strong>⇒</strong> 3x - 2x + 27 = 38</p><p><strong>⇒</strong><strong> </strong>3x - 2x = 38 - 27</p><p><strong>⇒</strong><strong> </strong>x = 38 - 27</p><p><strong>⇒</strong><strong> </strong><strong>x </strong><strong>=</strong><strong> </strong><strong>1</strong><strong>1</strong></p><p>The value of x is 11.</p><p><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u>_</u><u> </u></p><p></p><p>Finding, <u>The numerator and denominator-</u> </p><p><strong>Numerator</strong> <strong>:</strong><strong>-</strong></p><p>We assumed the numerator as <strong>(</strong><strong>x)</strong>.</p><p><strong>⇒</strong> x</p><p><strong>⇒</strong> 11</p><p><strong>Denominator</strong><strong> </strong><strong>:</strong><strong>-</strong></p><p>We assumed the denominator as <strong>(</strong><strong>x </strong><strong>+</strong><strong> </strong><strong>1</strong><strong>0</strong><strong>)</strong>.</p><p><strong>⇒</strong> (x + 10)</p><p><strong>⇒</strong> (11 + 10)</p><p><strong>⇒</strong> 21</p><p></p><p>Therefore, The fraction is - <strong>1</strong><strong>1</strong><strong>/</strong><strong>2</strong><strong>1</strong>.</p></body></html>

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5. The denominator of a rational number is greater than its numerator by 10. If the numerator is increased by 19 and the denominator is decreased by 1, the number obtained is ³/2. Find the rational number.​

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5. The denominator of a rational number is greater than its numerator by 10. If the numerator is increased by 19 and the denominator is decreased by 1, the number obtained is ³/2. Find the rational number.