The numerator of a fraction is less than its denominator by 2. If we subtract 2 from the numerator and add 2 to the denominator, then the new fraction is $$\frac{1}{3}$$​. What is the original fraction?

Correct option is D

Given:
Let numerator = x
Let denominator = x + 2 (since numerator is 2 less than denominator)
New fraction after changes = $$\frac 13$$​​
Solution:
​$$\frac{x - 2}{x + 2 + 2} = \frac{1}{3} \\\frac{x - 2}{x + 4} = \frac{1}{3} \\3(x - 2) = (x + 4) \\3x - 6 = x + 4 \\3x - x = 4 + 6 \\2x = 10 \\x = 5$$​​
So, Numerator = 5
Denominator = 5 + 2 = 7
Original fraction = $$\frac 57$$​​