$40\%$ of A is $60\%$ of B. $A:B$ will be:

Given the equation:
$$\frac{40}{100}\times A=\frac{60}{100}\times B$$

We can simplify this by multiplying both sides by $100$:

$$40A=60B$$

Now, solve for the ratio $\frac{A}{B}$:

$$\frac{A}{B}=\frac{60}{40}=\frac{3}{2}$$

Thus, the ratio $A:B$ is $3:2$.