Sum of digits of a two-digit number is 14. If 29 is subtracted from the number the digits of the
resulting number will be equal. Find the number.
Solution
The sum of the digits of a 2-digit number is 14. If 29 is subtracted from the number, the digits of
the resulting number are the same.
If the number is represented by xy, x + y = 14
=> x = 14 - y
10*x + y - 29 = 10C + C
=> 10(14 - y) + y - 29 = 11C
=> 140 - 10y + y - 29 = 11C
=> 111 - 9y = 11C
(111 - 9y) has to be an integral multiple of 11, this happens only when y = 5
The required number is 95.