Question

the denominator of a fraction is 1 more then twice its numerator. if the numerator and denominator are both increased by 5, it becomes 3/5 . find the original fraction ​

Answer 1

Answer:

Given :-

• The denominator of a fraction is 1 more than twice its numerator.
• If the numerator and denominator are both increase by 5, it becomes 3/5.

To Find :-

• What is the original number.

Solution :-

Let,

$\mapsto \bf{Numerator =\: x}$

$\mapsto \bf{Denominator =\: 2x + 1}$

Hence, the original fraction will be :

$\leadsto \sf\dfrac{Numerator}{Denominator}$

$\leadsto \sf\bold{\pink{\dfrac{x}{2x + 1}}}$

According to the question :

$\bigstar$ 5 is increase with both numerator and denominator, then the new number is 3/5.

$\implies \sf \dfrac{Numerator + 5}{Denominator + 5} =\: New\: Number$

$\implies \sf \dfrac{x + 5}{2x + 1 + 5} =\: \dfrac{3}{5}$

$\implies \sf \dfrac{x + 5}{2x + 6} =\: \dfrac{3}{5}$

By doing cross multiplication we get,

$\implies \sf 3(2x + 6) =\: 5(x + 5)$

$\implies \sf 6x + 18 =\: 5x + 25$

$\implies \sf 6x - 5x =\: 25 - 18$

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

Hence, the required original fraction is :

$\longrightarrow \sf Original\: Fraction =\: \dfrac{x}{2x + 1}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{7}{2(7) + 1}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{7}{14 + 1}$

$\longrightarrow \sf\bold{\red{Original\: Fraction =\: \dfrac{7}{15}}}$

${\small{\bold{\underline{\therefore\: The\: original\: fraction\: is\: \dfrac{7}{15}\: .}}}}$

Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that Numerator of a fraction be x

As it is given that the denominator of a fraction is 1 more then twice its numerator.

So, Denominator of a fraction = 1 + 2x

So, fraction is given by

$\rm :\longmapsto\:Fraction = \dfrac{x}{2x + 1}$

According to statement,

If numerator and denominator both are increased by 5.

So,

Numerator of a fraction = x + 5

and

Denominator of a fraction = 2x + 1 + 5 = 2x + 6

Now, fraction is given by

$\rm :\longmapsto\:Fraction = \dfrac{x + 5}{2x + 6}$

It is given that in this case,

$\rm :\longmapsto\:Fraction = \dfrac{3}{5}$

So,

$\rm :\longmapsto\:\dfrac{x + 5}{2x + 6} = \dfrac{3}{5}$

$\rm :\longmapsto\:5(x + 5) = 3(2x + 6)$

$\rm :\longmapsto\:5x + 25 = 6x + 18$

$\rm :\longmapsto\:5x - 6x = - 25+ 18$

$\rm :\longmapsto\: - x = -7$

$\bf\implies \:x = 7$

Therefore,

$\rm :\longmapsto\:Fraction = \dfrac{x}{2x + 1} = \dfrac{7}{2 \times 7 + 1} = \dfrac{7}{15}$