Question

A two digit number is exactly 5 times the sum of its two digit. what is that number?

Answer 1

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

Therefore, the final answer — 45.