The number is 32
Solution:
The number is 10y + x (original)
Let the units place be x
Let the tens place be y
The sum of a particular two digit number is 5
Therefore,
x + y = 5 ----- eqn 1
If this numbers digits are reversed, then the number is decreased by 9
numbers digits are reversed = 10x + y ( digits are reversed )
Then, the number is decreased by 9
10y + x - 9 = 10x + y
10y + x - 10x - y = 9
-9x + 9y = 9
Divide by 9 entire equation
-x + y = 1 ------- eqn 2
Add eqn 1 and eqn 2
x + y - x + y = 5 + 1
2y = 6
y = 3
Substitute y = 3 in eqn 2
-x + 3 = 1
-x = 1 - 3
-x = -2
x = 2
Thus the original number is:
Number = 32
