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).

The correct option is 12.

Let us solve the problem step-by-step:

Let the speed of the boat in still water be represented by $u$ and the speed of the stream by $v$.

According to the given ratio, the speed of the boat in still water to the speed of the stream is 5 : 1.
Thus, we can define them as:

$u=5x$

and

$v=x$

where $x$ is a constant multiplier.

The downstream speed of a boat is the sum of its speed in still water and the speed of the stream:
Downstream Speed = $u+v$

Substituting the values of $u$ and $v$ in terms of $x$:

Downstream Speed = $5x+x=6x$

We are given that the downstream speed is 18 km/h. Therefore, we can write:

$6x=18$

Solving for $x$:

$x=\frac{18}{6}=3$

The upstream speed of the boat is the difference between its speed in still water and the speed of the stream:
Upstream Speed = $u-v$

Substituting the values of $u$ and $v$ in terms of $x$:

Upstream Speed = $5x-x=4x$

Substituting the calculated value of $x=3$:

Upstream Speed = $4\times 3=12\text{km/h}$

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