A truck covers a distance of 510 km in 34 litres of diesel.

Let the required distance be x km. Then, we have:

Clearly, the less the quantity of diesel consumed, the less is the distance covered.

So, this is a case of direct proportion.

Now, $\frac{34}{510}=\frac{20}{x}$

$\Rightarrow \frac{1}{15}=\frac{20}{x}$

$\Rightarrow x \times 1=20 \times 15=300$

Therefore, the required distance is 300 km.