Let 10s digit of the number is x and unit digit of the number is y

So, the number = 10x + y

When the number is reversed = 10y + x

Given, nine times a two-digit number is the same as twice the number obtained by interchanging the digits of the number

=> 9(10x + y) = 2(10y + x)

=> 90x + 9y = 20y + 2x

=> 90x - 2x = 20y - 9y

=> 88x = 11y

=> y = 88x/11

=> y = 8x     .................1

Given, one digit of the number exceeds the other number by 7

=> y = x + 7

=> 8x = x + 7

=> 8x - x = 7

=> 7x = 7

=> x = 7/7

=> x = 1

Now, y = x + 7 = 1 + 7 = 8

So, the number = 10 * 1 + 8 = 10 + 8 = 18