Question

5. The denominator of a fraction is 4 more than twice the
numerator. When both the numerator and denominator
are decreased by 6, then the denominator becomes 12
times the numerator. Detemine the fraction.​

Answer 1

Solution :

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

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

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

A/q

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

&

The numerator = (r - 6)

The denominator = (m - 6)

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

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

$\longrightarrow\tt{m=2(7)+4}\\\\\\\longrightarrow\tt{m=14+4}\\\\\\\longrightarrow\tt{\blue{m=18}}$

Thus;

$\boxed{\bf{The\:fraction=\frac{r}{m}=\frac{7}{18} }}}}}$

Answer 2

${\bold{\huge{\blue{\underline{\pink{A}\purple{ns}\orange{wer}\red{!!!!!...}}}}}}$

let numerator be x and denomination be y.

$\bf\therefore\: Fraction= \dfrac{Numerator}{Denominator}$

$\bf\: fraction=\dfrac{x}{y}$

When denominator is 4 more than twice the number then,

$\bf\:y= 2x+4..................(i)$

when both numerator and denominator are decrease by 6 then,

Numerator = x - 6 and denominator = y - 6

when Denominator becomes 12 times the numerator then,

$\bf\: 12 (x-6)= y-6$

$\bf\implies\:12x-72= y-6$

$\bf\implies\:y=12x-72+6$

$\bf\implies\:y=12x-66$

Substitute equation (i),we get

$\bf\implies\:2x+4=12x-66$

$\bf\implies\:4+66=12x-2x$

$\bf\implies\:70=10x$

$\bf\implies\:x=\dfrac{70}{10}$

$\bf\implies\:x=7$

now,

putting equation (i)

$\bf\:y= 2x+4$

$\bf\implies\:y=2\times\:7+4$

$\bf\implies\:y=18$

now we have,

x = 7 and y = 18

$\bf\: Fraction= \dfrac{x}{y}$

$\bf\: Fraction=\dfrac{7}{18}$