The sum of the numerator and denominator of a fraction is $$8$$. If $$3$$ is added to both of the numerator and the denominator, the fraction becomes $$3/4$$. Find the fraction.
Let us consider, a fraction $$x/y$$, where $$x$$ is numerator and $$y$$ is denominator.
As per the statement,
$$x+y=8$$.....(1)
And,
$$(x+3)/(y+3)=3/4$$
$$4(x+3)=3(y+3)$$
$$4x-3y=-3$$....(2)
Using substitution method:
Substitute the values of $$x$$ from (1) in (2), we get
$$4(8-y)-3y=-3$$
$$32-4y-3y=-3$$
$$-7y=-35$$
or $$y=5$$
From (1): $$x+5=8$$
or $$x=3$$
Answer: Fraction is $$3/5$$