Question

The denominator of fraction is 4 more than twice the numerator. when both numerator and denominator are decreased by 6 then the denominator becomes 12 times the numerator . find the fraction​

Answer 1

Solution :

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

The denominator of fraction is 4 more than twice the numerator, when both numerator and denominator are decreased by 6 then the denominator becomes 12 times the numerator.

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

The fraction.

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

Let the numerator be r

Let the denominator be m

$\therefore{\boxed{\sf{The\:fraction\:is\:\:\dfrac{r}{m} }}}}$

A/q

$\leadsto\bf{m=2r+4......................(1)}$

&

$\longrightarrow\sf{12(r-6)=m-6}\\\\\longrightarrow\sf{12r-72=m-6}\\\\\longrightarrow\sf{12r-72=2r+4-6\:\:\:\:[from(1)]}\\\\\longrightarrow\sf{12r-72=2r-2}\\\\\longrightarrow\sf{12r-2r=-2+72}\\\\\longrightarrow\sf{10r=70}\\\\\longrightarrow\sf{r=\cancel{\dfrac{70}{10}} }\\\\\longrightarrow\sf{\green{r=7}}$

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

$\longrightarrow\sf{m=2(7)+4}\\\\\longrightarrow\sf{m=14+4}\\\\\longrightarrow\sf{\green{m=18}}$

Thus;

$\underbrace{\sf{The\:fraction\:is\:\:\dfrac{r}{m} =\dfrac{7}{18} }}}}$

Answer 2

Given,

• The denominator of a fraction is 4 more than twice the numerator.
• When we decrease the numerator and denominator both by 6 then the denominator becomes 12 times the numerator .

To Find,

• The Fraction

Solution,

⇒Suppose the Numerator be x

And , Suppose the Denominator be y

According to the First Condition :-

• The denominator of a fraction is 4 more than twice the numerator .

$\implies \boxed{\sf{y = 2x + 4}}$

According to the Second Condition :-

• When we decrease the numerator and denominator both by 6 then the denominator becomes 12 times the numerator .

$\implies \sf{(y - 6) = 12(x - 6)}$

$\implies \sf{y - 6 = 12x - 72}$

$\implies \sf{y - 12x = - 72 + 6}$

$\implies \sf{y - 12x = -66}$

$\implies \sf{2x + 4 - 12x = -66}$

$\implies \sf{-10x = -66 - 4}$

$\implies \sf{-10x = -70}$

$\implies \sf{x = \dfrac{70}{10}}$

$\implies \boxed{\sf{x = 7}}$

Now Put the Value of x in First Condition :-

$\implies \sf{y = 2x + 4}$

$\implies \sf{y =2(7) + 4}$

$\implies \sf{y = 14 + 4}$

$\implies \boxed{\sf{y = 18}}$

Therefore ,

$\boxed{\bold{\red{The \ Fraction = \dfrac{x}{y} = \dfrac{7}{18}}}}$

$\rule{200}2$