Let the two - digit number be xy (i.e. 10x + y).

After reversing the digits of the number xy, the new number becomes yx (i.e. 10y + x).

According to question -

(10x + y) + (10y + x) = 121

⇒ 11x + 11y = 121

⇒ x + y = 11.....(1)

and,

x - y = 3 or y - x = 3

[as we don't know which digit is greater out of x and y]

⇒ x - y = ±3.....(2)

Adding Equation (1) and (2), we get -

2x = 14 or 8

⇒ x = 7 or 4

Case 1. when x = 7

y = 4 [from equation (1)]

Case 2. when x = 4

y = 7 [from equation (1)]

Thus, the possible numbers are 47 or 74.