Question

Form the pair of linear equation for the following problems and find their solution by substituting method .
A fraction becomes $\frac{9}{11}$ if $2$ is added to both the numerator and the denominator . If $3$ is added to both the numerator and the denominator it becomes $\frac{5}{6}$ .Find the fraction .

Answer 1

If the Numerator is 'x' and denominator is 'y' , then the Fraction is $\frac{x}{y}$
Adding 2 to both Numerator and denominator , then fraction$\frac{9}{11}$
$11(x+2)=9(y+2)$
$11x+22=9y+18$
$11x-9y+22-18=0$
$11x-9y+4=\mathrm{0...}\left(i\right)$
Is 3 is added to both numerator and denominator , then ther fraction is $\frac{5}{6}$

$6(x+3)=5(y+3)$

$6x+18=5y+15$

$x=\frac{5y-3}{6}...\left(ii\right)$

substitute the value of $x$ in eqn (i)

$=11\times \frac{5y-3}{6}-9y+4=0$

$=\frac{55y-33}{6}-9y+4=0$

$=\frac{55y-33-54y+24}{6}=0$

$=y=9$

Substitute the value of $y$ in eq (ii)

$x=\frac{5\left(9\right)-3}{6}$

$x=7$

$\therefore$ fraction is $\frac{7}{9}$