When 16 is added to the denominator, the sum of the denominator and numerator has increased from 20 to 36

(20 + 16 = 36)


Since the fraction became 1/3, this means that the new denominator is now three times the numerator.

Let the numerator = 1 unit
Then, denominator = 3 units

Total = 1 unit + 3 units = 4 units

So 4 units = 36
1 unit = 36 ÷ 4 = 9

So this tells us that the numerator = 9
Original denominator = 20 - 9 = 11

The fraction written was 9/11.


Or

New denominator
= 3 units
= 3 x 9
= 27

Original denominator = 27 - 16 = 11



Check :


Original fraction : 9/11

New fraction : 9/(11 + 16)
= 9/27
= 1/3