Question

find the fraction, whose numerator is 4 less than the dinomenator if 1 is subtracted from numerator and 3 is added to the dinomenator fraction become 1/5 find the orignal fraction​

Answer 1

Given :

• The numerator of a fraction is 4 less than the denominator .
• If 1 is subtracted from numerator and 3 is added to the denominator the fraction becomes 1/5 .

To Find :

• Original Fraction .

Solution :

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

As Given that The numerator of a fraction is 4 less than the denominator . So ,

$\longmapsto\tt{Numerator=x-4}$

Now ,

• If 1 is subtracted from numerator and 3 is added to the denominator the fraction becomes 1/5 .

$\longmapsto\tt{Numerator=x-4-1=x-5}$

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

A.T.Q :

$\longmapsto\tt{\dfrac{x-5}{x+3}=\dfrac{1}{5}}$

$\longmapsto\tt{5(x-5)=1(x+3)}$

$\longmapsto\tt{5x-25=x+3}$

$\longmapsto\tt{5x-x=3+25}$

$\longmapsto\tt{4x=28}$

$\longmapsto\tt{x=\cancel\dfrac{28}{4}}$

$\longmapsto\tt\bf{x=7}$

Value of x is 7 .

Therefore :

$\longmapsto\tt{Numerator=7-4}$

$\longmapsto\tt\bf{3}$

$\longmapsto\tt{Denominator=x}$

$\longmapsto\tt\bf{7}$

So , The Fraction is 3/7 .

Answer 2

Answer:

Given :-

• The numerator of a fraction is 4 less than the denominator.
• 1 is subtracted from numerator and 3 is added to the denominator, the new fraction become 1/5.

To Find :-

• What is the original fraction.

Solution :-

$\bigstar$ The numerator of a fraction is 4 less than the denominator.

Let,

$\mapsto \bf Denominator =\: a$

$\mapsto \bf Numerator =\: a - 4$

Hence, the original fraction is :

$\leadsto \sf Original\: Fraction =\: \dfrac{Numerator}{Denominator}$

$\leadsto \sf\bold{\pink{Original\: Fraction =\: \dfrac{a - 4}{a}}}$

According to the question,

$\bigstar$ 1 is subtracted from numerator and 3 is added to the denominator, the new fraction become 1/5.

$\implies \bf \dfrac{Numerator - 1}{Denominator + 3} =\: New\: Fraction$

$\implies \sf \dfrac{a - 4 - 1}{a + 3} =\: \dfrac{1}{5}$

$\implies \sf \dfrac{a - 5}{a + 3} =\: \dfrac{1}{5}$

By doing cross multiplication we get,

$\implies \sf 5(a - 5) =\: 1(a + 3)$

$\implies \sf 5a - 25 =\: a + 3$

$\implies \sf 5a - a =\: 3 + 25$

$\implies \sf 4a =\: 28$

$\implies \sf a =\: \dfrac{\cancel{28}}{\cancel{4}}$

$\implies \sf a =\: \dfrac{7}{1}$

$\implies \sf\bold{\purple{a =\: 7}}$

Hence, the required original fraction will be :

$\longrightarrow \sf Original\: Fraction =\: \dfrac{a - 4}{a}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{7 - 4}{7}$

$\longrightarrow \sf\bold{\red{Original\: Fraction =\: \dfrac{3}{7}}}$

${\small{\bold{\underline{\therefore\: The\: original\: fraction\: is\: \dfrac{3}{7}\: .}}}}$