In a positive number of two digits,the sum of the digit is 15. If the digits are interchanged,the number is increased by 9. What is the number?
Let the tens digit be x and the units digit be y.
So, the original number is 10x + y and the reversed number is 10y + x.
According to the given conditions:
1. x + y = 15
2. 10y + x = 10x + y + 9
From equation 1:
y = 15 - x
Substitute y = 15 - x into equation 2:
10(15 - x) + x = 10x + 15 - x + 9
150 - 10x + x = 10x + 24
150 - 9x = 10x + 24
126 = 19x
x = 6.63 (approx.)
Since x has to be a digit, we take x = 6.
So, y = 15 - 6 = 9.
Therefore, the original number is 69.