Condition 1: Sum of the original number and number obtained by reversing it = 165
Original number + New number = 165
By substituting the values we get,
(10x+y)+(10y+x) = 165 ------------ (1)
Condition 2: The digits of the original number differs by 3
x - y = 3 ---------------- (2) (since, it's given that ten's digit > one's digit)
From equation (1)
11x + 11y = 165
Dividing by 11 on both the sides we get,
x + y = 15 --------------- (3)
By adding equation (2) and (3) we get,
x - y + x + y = 3 + 15
⇒ 2x = 18
⇒ x = 9
⇒ y = 15 - 9 = 6
Hence the original number is 10x + y = 10(9) + 6 = 96
Verification:
We can verify the result by substituting the values in the given conditions:
96 + 69 = 165
9 - 6 = 3
Hence, both the conditions are satisfied.