The sum of the digits of a two-digit number is 7. If 9 is subtracted from the number, then the digits interchange their places. Find the number?

Let the number be 10x+y

x is in the 10s place y is in the 1s place

given x+y=7 ---Eq 1

10x+y-9=10y+x

9x-9y=9

9(x-y)=9(Taking 9 common)

x-y=1 -------Eq 2

Eq 1 + Eq 2 We get

2x=8

x=4

x+y=7

4+y=7

y=3

The required number is 10x+y=10(4) +3

=40+3

=43

Thumbs up pls