Question 148904
Let a and b the digits we can write the number as "ab" but the number is 10*a+b
(for example if a=3 and b=2 the number would be 32 and 32 =10*3+2)


a two digit number is 5 times the sum of its digit then 10*a+b=5(a+b)
when 9 is added to the number the result is the original number with its reversed 10*a+b+9=10*b+a

then we have the following equations:

10*a+b=5(a+b)
10*a+b+9=10*b+a

then

10a+b=5a+5b
10a+b+9=10b+a

then

5a-4b=0
9a-9b=-9

then

5a-4b=0
a-b=-1

then using 2nd eq a=b-1

using 1st eq 5(b-1)-4b=0

then 5b-5-4b=0
then b=5 and a=5-1=4

so the original number is 45