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