The total amount of $49$ is distributed among A, B, and C. A receives $5$ more than B and B receives $4$ more than C. What is the ratio of their shares?

Let the share of C be $x$.
According to the problem statement:

* B's share = $x+4$
* A's share = $\text{B’s share}+5=(x+4)+5=x+9$

The sum of all their shares is equal to $49$:

$$A+B+C=49$$

$$(x+9)+(x+4)+x=49$$

$$3x+13=49$$

$$3x=49-13$$

$$3x=36$$

$$x=12$$

Now, let's calculate the individual shares:

* C's share = $12$
* B's share = $12+4=16$
* A's share = $12+9=21$

The ratio of their shares $A:B:C$ is:

$$21:16:12$$