Question

If 2 is added to the numerator of a fraction,it reduces to $\left(\frac{2}{3}\right)$ and if 1 is subtracted from the denominator,it reduces to $\left(\frac{1}{2}\right)$.Find the fraction.

Answer 1

Let x be in the numerator and y denominator

fraction: $\frac{x}{y}$

Case 1:

$\frac{x+2}{y}=\frac{2}{3}3(x+2)=2y3x+6=2y3x-2y=-6-----\left(1\right)$

Case 2:

$\frac{x}{(y-1)}=\frac{1}{3}3x=y-13x-y=-1-----\left(2\right)multiply\left(2\right)by-2-4x+2y=+2addto\left(1\right)-x=-4numerator,x=4putvalueofyin\left(2\right)y=9\therefore \frac{4}{9}isthefraction$