A person can row $22\frac{1}{2}\text{km}$ an hour in still water and he finds that it takes him twice as long to row up as to row down the stream. The speed of the stream is:

Let the speed of the boat in still water be $u=22\frac{1}{2}=22.5\text{km/h}$.
Let the speed of the stream be $v\text{km/h}$.

* Downstream speed = $u+v=22.5+v$
* Upstream speed = $u-v=22.5-v$

The question states that the time taken to go upstream is twice the time taken to go downstream for the same distance. Since time is inversely proportional to speed when distance is constant:

$$\text{Downstream speed}=2\times \text{Upstream speed}$$

$$22.5+v=2(22.5-v)$$

$$22.5+v=45-2v$$

$$v+2v=45-22.5$$

$$3v=22.5$$

$$v=\frac{22.5}{3}=7.5=7\frac{1}{2}\text{km/h}$$