Question

A fraction becomes $\frac{4}{5}$ when 1 is added to each numerator and denominator. However, if we subtract 5 from each then it becomes $\frac{1}{2}$. Find the fraction. [3 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 1 Mark

Let the numerator be $x$ & the denominator be $y$

Then according to the given condition,

$\frac{(x+1)}{(y+1)}=\frac{4}{5}$

$\Rightarrow 5x+1=4y\dots \dots \left(i\right)$

$\frac{(x-5)}{(y-5)}=\frac{1}{2}$

$\Rightarrow y=2x-5\dots \dots \left(ii\right)$

From (i) and (ii) we get,

$5x+1=4(2x-5)$

$5x+1=8x-20$

$3x=21$

$x=7$

$y=2x-5$

$y=14-5=9$

$x=7,y=9$