Let's assume the original number is 10x + y, where x and y are the two digits.
Given that the sum of the two digits is 11, we have x + y = 11.
When the digits are interchanged, the number becomes 10y + x.
According to the second condition, the original number (10x + y) increased by 9 is equal to the number with the digits interchanged (10y + x). So, we have:
10x + y + 9 = 10y + x.
Now, substitute the value of x + y from the first condition into the above equation:
10(11 - y) + y + 9 = 10y + 11 - y
110 - 10y + y + 9 = 10y + 11 - y
110 + 9 = 11y + 11
119 = 11y
y = 119 / 11
y = 9
Now that we have found the value of y, we can substitute it back into x + y = 11 to find the value of x:
x + 9 = 11
x = 11 - 9
x = 2
Therefore, the original number is 29.
A nu.Ber is made IP if two digits. The sum of the two digits is 11. If the digits are interchanged the original number is increased by nine. What is the number
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