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.

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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.

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