# The sum of the digits in a two-digits number is 9. The number obtained by interchanging the digits exceeds the original number by 27. Find the two-digit number.

Let the unit digit be 'x'

Let the digit at ten's place be 'y'

The original number will be 10y + x

Given,

Sum of digits = 9

x + y = 9

x = 9 - y eq.[1]

Also,

If the digits are interchanged,

Reversed number will be = 10x + y

As, reversed number exceeds the original number by 27,

(10x + y) - (10y + x) = 27

10x + y - 10y - x = 27

9x - 9y = 27

x - y = 3

9 - y - y = 3 eq.[using 1]

-2y = -6

y = 3

Using this in eq.[1]

x = 9 - 3 = 6

Hence the original number is 10y + x = 10(3) + 6 = 30 + 6 = 36.

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