The sum of the digits of a 2-digit number is 7. reversing the digit increase the number by 9. Find the numbers?

Let the numbers be xy = a

Then the reverse number will be yx = b.

Given the sum of the digits = 7

==> x + y = 7

==> y= 7-x.............(1).

==> b-a = 9

==> (7-x)x - x(7-x) = 9

==> (7-x)*10 + x = b

==> 70-10x + x = b

==> 70-9x = b...........(1)

==> x*10+ (7-x) = b.

But b-a = 9 ==> a= b-9

==> x*10+ (7-x) = b-9

==> 10x + 7 - x + 9 = b

==> 9x + 16 = b..............(2)

We will add (1) and (2).

==> 86 = 2b

==> b= 43

==> a= 34

==> Then, the two digit number is 34.

To check:

3+ 4 = 7

Also, 43 - 34 = 9