The sum of digits of a two-digit number is 9. When the digits are reversed, the number decreases by 45. Find the changed number.

Let say, the number is 'ab'.

So, ab can be rewrite as (10a+b).

if we reverse its digits ,the number will become 'ba' or (10b+a).

According to question ,

$$\left(10a+b\right)-\left(10b+a\right)=45.$$

or,$$9a-9b=45.$$

or,$$a-b=5.$$........................(1)

But sum of digits is 9 ;

So,a+b=9...............................(2)

Now (1)+(2) :

$$2a=14$$

or, a=7.

Put a=7 in (1) :

b=2.

So, original number is 72 and changed number is 27.

D is correct choice.