The speed of the man in downstream is 15 km/hr and the speed of the stream is 3 km/hr. Quantity I. The man's speed against the current. Quantity II. Average of upstream and downstream speed.

The correct option is: Quantity I < Quantity II.

Let us analyze and calculate the two quantities step-by-step to compare them.

We are given:
Speed of the man downstream (denoted as $S_d$) = 15 km/hr
Speed of the stream (denoted as $v$) = 3 km/hr

First, we need to find the speed of the man in still water (denoted as $u$).
We know that:
$S_d=u+v$
Substituting the given values:
$15=u+3$
Solving for $u$:
$u=15-3=12$ km/hr

Now, we can find the upstream speed of the man (speed against the current, denoted as $S_u$).
The upstream speed is given by:
$S_u=u-v$
Substituting the values of $u$ and $v$:
$S_u=12-3=9$ km/hr

Let us evaluate Quantity I:
Quantity I represents the man's speed against the current (upstream speed).
Therefore, Quantity I = 9 km/hr.

Let us evaluate Quantity II:
Quantity II represents the average of the upstream and downstream speeds.
Average speed = $\frac{S_u+S_d}{2}$
Substituting the values of $S_u=9$ km/hr and $S_d=15$ km/hr:
$\text{Average speed}=\frac{9+15}{2}=\frac{24}{2}=12$ km/hr
Therefore, Quantity II = 12 km/hr.

Comparing the two quantities:
Quantity I = 9
Quantity II = 12
Since 9 < 12, we have:
Quantity I < Quantity II