Question

In a Fraction,twice the numerator is 2 more than denominator. If 3 is added to the numerator and to the denominator, the new fraction is 2by 3 find the original fraction.​

Answer 1

Answer:

Given :-

• If a fraction, twice the numerator is 2 more than denominator. If 3 is added to the numerator and to the denominator, the new fraction 2/3.

To Find :-

• What is the original fraction.

Solution :-

Let,

$\mapsto \sf\bold{Numerator =\: x}$

$\mapsto \sf\bold{Denominator =\: 2x - 2}$

Then, the original fraction is :

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

$\leadsto \sf\bold{\pink{\dfrac{x}{2x - 2}}}$

According to the question,

$\implies \sf \dfrac{Numerator + 3}{Denominator + 3} =\: New\: fraction$

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

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

By doing cross multiplication we get,

$\implies \sf 2(2x + 1) =\: 3(x + 3)$

$\implies \sf 4x + 2 =\: 3x + 9$

$\implies \sf 4x - 3x =\: 9 - 2$

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

Hence, the required original fraction is :

$\longrightarrow \sf \dfrac{x}{2x - 2}$

$\longrightarrow \sf \dfrac{7}{2(7) - 2}$

$\longrightarrow \sf \dfrac{7}{2 \times 7 - 2}$

$\longrightarrow \sf \dfrac{7}{14 - 2}$

$\longrightarrow \sf\bold{\red{\dfrac{7}{12}}}$

${\normalsize{\bold{\underline{\therefore\: The\: original\: fraction\: is\: \dfrac{7}{12}\: .}}}}$