Question

sum of the digits of a two-digit number is 9 the number obtained by interchanging the digits exceeds the given number by 27 find the given number

Answer 1

x+y=9
x=9-y(1)
10x+y+27=10y+x
9x+27=9y
9(9-y)+27=9y
81-9y+27=9y
108=18y
6=y
using it in (1)
x=3
so no is 36
and the no obtained by reversing its digits is 63

Answer 2

Let the given number be
$10x + y$

Given:

$(10y + x) - (10x + y) = 27 \\ 9y - 9x = 27 \\ y - x = 3$
Also
$x + y = 9$
solving we get

$x = 3 \\ y = 6$
The required number is 36

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