Step 1: Analyze structure A.
In structure A, benzene contains one bromo group and one \( 1\text{-methylpropyl} \) group.
The \( 1\text{-methylpropyl} \) group is attached at the ortho position with respect to bromine.
Therefore, the IUPAC name is:
\[
1\text{-Bromo-}2\text{-(}1\text{-methylpropyl)benzene}
\]
So:
\[
A = R
\]
Step 2: Analyze structure B.
In structure B, benzene contains \( CH_2Br \) group and \( CH_2-C(CH_3)_3 \) group.
The substituent \( CH_2-C(CH_3)_3 \) is \( 2,2\text{-dimethylpropyl} \).
Thus, the correct IUPAC name is:
\[
1\text{-Bromomethyl-}3\text{-(}2,2\text{-dimethylpropyl)benzene}
\]
So:
\[
B = P
\]
Step 3: Analyze structure C.
In structure C, benzene contains bromine and \( 2\text{-methylpropyl} \) group.
The two groups are present at para positions.
Therefore, the correct IUPAC name is:
\[
1\text{-Bromo-}4\text{-(}2\text{-methylpropyl)benzene}
\]
So:
\[
C = S
\]
Step 4: Analyze structure D.
In structure D, benzene contains bromine and \( 1\text{-methylethyl} \) group.
The \( 1\text{-methylethyl} \) group is also called isopropyl group.
Both groups are present at para positions.
Therefore, the correct IUPAC name is:
\[
1\text{-Bromo-}4\text{-(}1\text{-methylethyl)benzene}
\]
So:
\[
D = Q
\]
Step 5: Write the complete matching.
From the above analysis:
\[
A = R,\quad B = P,\quad C = S,\quad D = Q
\]
Step 6: Match with the given options.
The matching \( A = R,\; B = P,\; C = S,\; D = Q \) corresponds to option (A).
Step 7: Conclusion.
Thus, the correct match is:
\[
\boxed{A = R,\; B = P,\; C = S,\; D = Q}
\]