Question

the sum of the digits of a 2 digit number is 9 the number obtained by reversing the order of digits of the given number exceeds the given number by 27 find the given number

Answer 1

Let the digits of a two digit number be x and y

Given that

x+y=9

y=9-x

The original number is

10x+y

Substitute y with 9-x

10x+(9-x)

=10x-x+9

=9x+9

The number formed when reversing the digits is

10y+x

Substitute y with 9-x

10 (9-x)+x

90-10x+x

90-9x

Given that the reverse digit exceeds the original number by 27

Original number+27=reverse number

(9x+9)+27=90-9x

9x+9x=90-9-27

18x=54

x=54/18

x=3

The original given number is

9x+9=9*3+9

=36

Confirmation

Reverse number=63

63 exceeds 36 by 27

63-36=27

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