Question

The numerator of a fraction is $4$ less than the denominator. If the numerator is decreased by $2$ and denominator is increased by $1$, then the denominator is eight times the numerator. The fraction is also written as $\frac{m}{14}$. What is the value of m?

Answer 1

Let the numerator be x & denominator be y

according to question

CASE 1 :

$x=y-4$

$x=y-4..............\left(1\right)$

CASE 2 :

$8(x-2)=y+1$

$8x-y=17\dots \dots \dots ...\left(2\right)$

from (1)

$8(y-4)-y=17$

$8y-32-y=17$

$7y=49$

$y=7$

from (1)

$x=y-4\Rightarrow 3$

thus

$Fraction=\frac{x}{y}=\frac{3}{7}$

according to question fraction is of the form$\frac{m}{14}$

$\Rightarrow \frac{3}{7}\times \frac{2}{2}=\frac{6}{14}\iff \frac{m}{14}$

$\therefore m=6$