Given, velocity of sound, $v=330 \mathrm{~m} / \mathrm{s}$
Let frequency of horn be $f$ and speed of the car be $v_{c}$. The frequency of the horn of the car heard by the policeman before it crosses him is given as
$$
f^{\prime}=f\left(\frac{v}{v-v_{c}}\right) \quad \text{...(i)}
$$
and after it crosses him is given as
$$
f^{\prime \prime}=f\left(\frac{v}{v+v_{c}}\right) \quad \text{...(ii)}
$$
From Eqs. (i) and (ii), we get
$$
\begin{aligned}
\frac{f^{\prime \prime}}{f^{\prime}} &=\frac{v-v_{c}}{v+v_{c}}=\frac{330-v_{c}}{330+v_{c}} \\
\Rightarrow \quad \frac{f^{\prime \prime}}{f^{\prime}} &=\frac{330-v_{c}}{330+v_{c}} \quad \text{...(iii)}
\end{aligned}
$$
Since, $f^{\prime \prime}=f^{\prime}-15 \%$ of $f^{\prime}=0.85 f^{\prime}$
$\therefore$ From Eq. (iii), we get
$$
\frac{0.85 f^{\prime}}{f^{\prime}}=\frac{330-v_{c}}{330+v_{c}}
$$
$$
\Rightarrow \quad 0.85=\frac{330-v_{c}}{330+v_{c}} \Rightarrow v_{c}=26.7 \mathrm{~ms}^{-1}
$$