Answer:
56
Explanation:
let the 2 digits be a and b
Create 2 equations, solve simultaneously for a and b
a + b = 11 → ( 1) ( sum of digits )
The original number is ab, that is 10a + b ( considering place value )
Interchanging the 2 digits gives ba, that is 10b + a, thus
10b + a = 10a + b + 9 ( original number increased by 9 )
Subtract b from both sides
9b + a = 10a + 9 ( subtract 10a from both sides )
9b - 9a = 9 → (2)
Rearranging (1) expressing a in terms of b
a = 11 - b
Substitute a = 11 - b into (2)
9b - 9(11 - b) = 9 ← distribute and simplify left side
9b - 99 + 9b = 9
18b - 99 = 9 ( add 99 to both sides )
18b = 108 ( divide both sides by 18 )
b = 6
Substitute b = 6 into (1)
a + 6 = 11 ⇒ a = 5
The original number is 56