If $30\%$ of $(B-A)=18\%$ of $(A+B)$, then the ratio $A:B$ will be

We are given the relationship:
$$30\%\times (B-A)=18\%\times (A+B)$$
Eliminating the percentage signs from both sides:
$$30(B-A)=18(A+B)$$
Divide both sides by 6:
$$5(B-A)=3(A+B)$$
Expand the brackets:
$$5B-5A=3A+3B$$
Rearrange terms to group $A$ and $B$:
$$5B-3B=3A+5A$$
$$2B=8A$$
Find the ratio $\frac{A}{B}$:
$$\frac{A}{B}=\frac{2}{8}=\frac{1}{4}$$
Thus, $A:B=1:4$.