Explanation:
Let x be the fraction's numerator.
Then (x + 7) is the fraction's denominator.
Numerator increased by 1 => (x + 1)
Denominator decreased by 2 => (x + 5)
We have (x + 1) / (x + 5) = 3/5.
Therefore by cross-multiplication,
3(x + 5) = 5(x + 1).
=> 3x + 15 = 5x + 5
=> 2x = 10
=> x = 5.
Hence the original fraction is 5/12.