Question

A two digits number is such that the sum of its digits is 9 also the original number is 9 more than the number formed by the reversing the digits . Find the number

Answer 1

one's digit = x

ten's digit = y

x + y = 9..............1

10y + x = 10x + y + 9

10y - y + x -10x = 9

9y - 9x = 9

y - x = 1.......2

from 1 and 2 

2y = 10
y = 5

x + y = 9
x + 5 = 9
x = 4

tens digit  = 5 ones digit = 4

number is 54

Answer 2

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one's digit = x

ten's digit = y

x + y = 9..1

10y + x = 10x + y + 9

10y - y + x -10x = 9

9y - 9x = 9

y - x = 1..2

from 1 and 2 

2y = 10

y = 5

x + y = 9

x + 5 = 9

x = 4

tens digit  = 5 ones digit = 4

number is 54