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Question

If the numerator of a fraction is increased by 2 and the denominator by 1 it becomes 1. Again, if the numerator decreased by 4 and the denominator by 2 it becomes 1/2 Find the fraction.

4/5

5/6

6/7

7/8

ANSWER : 4

Descrption

Let, the fraction is&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mi>y</mi></mfrac></math>ATQ,&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>x</mi><mo>+</mo><mn>2</mn></mrow><mrow><mi>y</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mn>1</mn></math> Multiplying both sides by y+1 x + 2 = y + 1 x = y - 1&lt;math xmlns="http://www.w3.org/1998/Math/MathML"&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mfrac&gt;&lt;mspace linebreak="newline"/&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mspace linebreak="newline"/&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mspace linebreak="newline"/&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/math&gt; Inserting x = y-1 to equation above 2(y-1)= y+6 2y-2 = y+6 y = 8Using x = y - 1 x = 8 - 1 x = 7&nbsp;so&nbsp;<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>x</mi><mi>y</mi></mfrac><mo>=</mo><mfrac><mn>7</mn><mn>8</mn></mfrac></math>

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