Question

​13. If 2 is subtracted from the numerator and 1 is added to the denominator, a fraction becomes 1/2 but when 4 is added to the numerator and 3 is subtracted from the denominator, it becomes 3/2. Find the fraction.

Answer 1

Dear Student,


Let , fraction = $\frac{x}{y}$

From first condition we get :

$\frac{x-2}{y+1}=\frac{1}{2}$
$\Rightarrow$ 2 x - 4 = y + 1

$\Rightarrow$ 2x - y = 5 --- ( 1 )

And from second condition we get :

$\frac{x+4}{y-3}=\frac{3}{2}$
$\Rightarrow$ 2 x + 8 = 3 y - 9

$\Rightarrow$ 2x - 3 y = - 17 --- ( 2 )

Now we subtract equation 2 from equation 1 and get

2 y = 22

y = 11 , Substitute in equation 1 we get

2 x - 11 = 5

2 x = 16

x = 8

Therefore,

fraction = $\frac{\mathbf{8}}{\mathbf{11}}$


Regards