The ratio of the speed of a boat in still water to the speed of the stream is 5 : 1. If the downstream speed of the boat is 18 km/h, find the upstream speed (in km/hr).

To find the upstream speed of the boat, let us break down the problem step-by-step using the relationship between the speed of the boat in still water, the speed of the stream, and the speeds of the boat moving downstream and upstream.

Let the speed of the boat in still water be represented by $x$ and the speed of the stream be represented by $y$.

According to the problem, the ratio of the speed of the boat in still water to the speed of the stream is $5:1$. Therefore, we can express $x$ and $y$ in terms of a common variable $k$:
$x=5k$
$y=1k=k$

The downstream speed of the boat is the speed of the boat in still water plus the speed of the stream:
$\text{Downstream Speed}=x+y$

Substituting the values in terms of $k$:
$\text{Downstream Speed}=5k+k=6k$

We are given that the downstream speed is 18 km/h. Therefore:
$6k=18$

Solving for $k$:
$k=\frac{18}{6}=3$

Now we can determine the individual speeds:
Speed of the boat in still water, $x=5\times 3=15\text{km/h}$
Speed of the stream, $y=3\text{km/h}$

The upstream speed of the boat is the speed of the boat in still water minus the speed of the stream:
$\text{Upstream Speed}=x-y$

Substituting the calculated values:
$\text{Upstream Speed}=15-3=12\text{km/h}$

Thus, the upstream speed of the boat is 12 km/h.