Question

The denominator of a fraction is 1 more than double of the numerator.If both the numerator and the denominator are increased by 4 ,the fraction becomes 3/5.Assuming the numerator to be x,form an equation. Also find the fraction. ​

Answer 1

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Answer 2

Solution :

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

The denominator of a fraction is 1 more than double of the numerator.If both the numerator and the denominator are increased by 4,the fraction becomes 3/5.

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

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

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

&

$\longrightarrow\sf{\dfrac{r+4}{m+4} =\dfrac{3}{5} }\\\\\\\longrightarrow\sf{5(r+4)=3(m+4)}\\\\\\\longrightarrow\sf{5r+20=3m+12}\\\\\\\longrightarrow\sf{5r-3m=12-20}\\\\\\\longrightarrow\sf{5r-3m=-8}\\\\\\\longrightarrow\sf{5r-3(2r+1)=-8\:\:\:[from(1)]}\\\\\\\longrightarrow\sf{5r-6r-3=-8}\\\\\\\longrightarrow\sf{-r=-8+3}\\\\\\\longrightarrow\sf{\cancel{-}r=\cancel{-}5}\\\\\\\longrightarrow\sf{\blue{r=5}}$

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

$\longrightarrow\sf{m=2(5)+1}\\\\\longrightarrow\sf{m=10+1}\\\\\longrightarrow\sf{\blue{m=11}}$

Thus;

$\boxed{\bf{The\:fraction=\frac{r}{m} =\frac{5}{11} }}}}$