Question

sum of denominator and numerator of fraction is 4 more than twice numerator if numerator and deniminator increased by 3 they are in ratio 2 ratio 3 find fraction

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Answer 1

Step-by-step explanation:

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Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

Sum of denominator and numerator of fraction is 4 more than twice numerator if numerator and denominator increased by 3, they are in the ratio 2:3.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The fraction.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the numerator be r

Let the denominator be m

$\boxed{\bf{The\:fraction\:=\frac{r}{m} }}}}$

A/q

$\longrightarrow\sf{r+m=2r+4}\\\\\longrightarrow\sf{m=2r+4-r}\\\\\longrightarrow\sf{m=r+4....................(1)}$

&

$\longrightarrow\sf{\dfrac{r+3}{m+3} =\dfrac{2}{3} }\\\\\\\longrightarrow\sf{3(r+3)=2(m+3)}\\\\\\\longrightarrow\sf{3r+9=2m+6}\\\\\\\longrightarrow\sf{3r-2m=6-9}\\\\\\\longrightarrow\sf{3r-2m=-3}\\\\\\\longrightarrow\sf{3r-2(r+4)=-3\:\:\:[from(1)]}\\\\\\\longrightarrow\sf{3r-2r-8=-3}\\\\\\\longrightarrow\sf{r=-3+8}\\\\\\\longrightarrow\sf{\orange{r=5}}$

Putting the value of r in equation (1),we get;

$\longrightarrow\sf{m=5+4}\\\\\longrightarrow\sf{\orange{m=9}}$

Thus;

$\boxed{\bf{The\:fraction\:=\frac{r}{m}=\frac{5}{9} }}}}$