Given information:
- 54g of A contains 1.5 times the number of atoms in 4g of A.
- 18g of B is equivalent to the same number of atoms as 4g of A.

Calculating the number of atoms in 54g of A:
To find the number of atoms in 54g of A, we first need to determine the number of atoms in 4g of A.

Let's assume that there are 'x' atoms in 4g of A.
So, the number of atoms in 54g of A can be calculated as follows:

Number of atoms in 54g of A = (Number of atoms in 4g of A) * (54g / 4g)
= x * 13.5

Given that 54g of A contains 1.5 times the number of atoms in 4g of A, we can write the equation as:

x * 13.5 = 1.5x

Simplifying the equation, we get:

13.5 = 1.5

This equation is not possible, which means there is an error in the given information.

However, if we assume that the information provided is incorrect, we can proceed to find the ratio of the atomic weights of A and B.

Calculating the ratio of atomic weights:
Let's assume that the atomic weight of A is 'M' and the atomic weight of B is 'N'.

Given that 18g of B is equivalent to the same number of atoms as 4g of A, we can write the equation as:

(N * 18g) = (M * 4g)

Dividing both sides of the equation by 4g, we get:

N = (M * 4g) / 18g

Simplifying further, we have:

N = (2M) / 9

Therefore, the ratio of the atomic weights of A and B is:

M : N = M : (2M/9) or 9M : 2M