Solution:
Let the ages of Sachin and Amit be $7 x$ and $4 x$.
From the question,
$$
\begin{aligned}
& 7 x+4 x=33 \\
\Rightarrow & 11 x=33 \\
\therefore \quad & x=\frac{33}{11}=3 \text { years }
\end{aligned}
$$
Now, the Age of Sachin $=7 x$
$$
\begin{aligned}
&=7 \times 3 \\
&=21 \text { years } \\
\& \text { the age of Amit } &=4 \times \\
&=4 \times 3 \\
&=12 \text { years }
\end{aligned}
$$
$$
\text { Befor } 6 \text { years their ages will be }
$$
$21-6=15$ years $\& 12-6=6$ years
$\therefore \quad$ Ratio $=\frac{15}{6}=\frac{5}{2}=5: 2 ;$ Ans.
$\therefore \quad$ Correct option is $(\mathrm{d})$
Trick :
Sachin : Amit
$$
\begin{array}{l}
\quad 7 \quad: 4 \\
\Rightarrow \quad: 7+4=33 \\
\Rightarrow \quad 1=3 \\
\Rightarrow \quad: 2=6 \\
\therefore \quad \text { After } 6 \text { years the required } \\
\text { Patio }=(7-2):(4-2)=5: 2 ; \text { Ans. }
\end{array}
$$
