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.

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.