Question

We add 1 to numerator and subtract 1 from the denominator a fraction becomes 1 . it also becomes 1/2 if we add 1 to the denominator , then the sum of the numerator and the denominator of the fraction is?

Answer 1

Let the fraction be
$\frac{x}{y}$
1 added to numerator and 1 subtracted from denominator answer is 1
Hence
$\frac{x + 1}{y - 1} = 1 \\ x + 1 = y - 1 \\ x - y = - 2$
By second condition
If 1 is added to denominator
fraction becomes 1/2
Hence
$\frac{x}{y + 1} = \frac{1}{2} \\ 2x = y + 1$
But y=x+2
hence
$2x = x + 2 + 1 \\ x = 3$
Put in i
$2x = y + 1 \\ 2 \times 3 = y + 1 \\ y = 5$
We have to find x+y
hence
$x + y \\ = 5 + 3 \\ = 8$