Question

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Answer 1

Let the digit in unit's place be x.

Let the digit in ten's place be y.

Therefore the required decimal expansion = (10y + x).

if the order of digits is reversed, the reversing number = 10x + y.

Given that sum of the digits of a two-digit number = 9.

x + y = 9  ----- (1) 

Given that number obtained by interchanging the digits exceeds the number by 27.

10x + y = 10y + x + 27

10x + y - 10y - x = 27

9x - 9y = 27

x - y = 3   ------ (2)

On solving (1) & (2), we get

x + y = 9

x - y = 3

-------------

2x = 12

x = 6

Substitute x = 6 in (1), we get

x + y = 9

6 + y = 9

y = 3.

Therefore the required number = 10y + x

                                                     = 10 * 3 + 6

                                                     = 36.


Hence, the number is 36.


Hope this helps! 

Answer 2

Hi,

Please see the attached file!

Thanks