Concept:
The minimum length of transition curve based on the permissible rate of change of superelevation is
\[
\boxed{
L=N \times W \times e
}
\]
where
\[
N=\text{Rate of change of superelevation},
\]
\[
W=\text{Width of pavement},
\]
\[
e=\text{Superelevation}.
\]
Step 1: Write the given data.
\[
N=120
\]
\[
W=10\text{ m}
\]
\[
e=\frac{1}{15}
\]
Step 2: Calculate the transition length.
\[
L
=
120\times10\times\frac{1}{15}
=
80\text{ m}
\]
Hence,
\[
\boxed{L=80\text{ m}}
\]
Therefore, the correct option is
\[
\boxed{(C)\;80\text{ m}.}
\]