Question

the denominator of a fraction is 12 more than the numerator. If 3 is added to the denominator and 5 is added to the numerator, then the fraction is 3/4. Find the original fraction.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given :

• Denominator of a fraction is 12 more than the numerator.
• If numerator is increased by 5 and denominator is increased by 3 then the number obtained is 3/4 .

To Find :

• The Fraction .

Solution :

$\longmapsto\tt{Let\:Numerator\:be=x}$

As Given that Denominator of a fraction is 12 more than the numerator. So ,

$\longmapsto\tt{Denominator=x+12}$

Now ,

• If numerator is increased by 5 and denominator is decreased by 3 then the number obtained is 3/4 .

$\longmapsto\tt{Numerator=x+5}$

$\longmapsto\tt{Denominator=x+3+12=x+15}$

A.T.Q :

$\longmapsto\tt{\dfrac{x+5}{x+15}=\dfrac{3}{4}}$

$\longmapsto\tt{4(x+5)=3(x+15)}$

$\longmapsto\tt{4x+20=3x+45}$

$\longmapsto\tt{4x-3x=45-20}$

$\longmapsto\tt{1x=25}$

$\longmapsto\tt\bf{x=25}$

Value of x is 25 ..

Therefore :

$\longmapsto\tt\bf{Numerator=25}$

$\longmapsto\tt{Denominator=25+12}$

$\longmapsto\tt\bf{37}$

So , The Rational Number is 25/37 ..