Water sample is called cleanest on the basis of which one of the BOD values given below:

First, remember the definition: the biochemical oxygen demand, written as $$\text{BOD}$$, measures the amount of dissolved oxygen required by microorganisms to oxidise the organic matter present in a water sample.

A key point is that a high concentration of biodegradable organic impurities will make microorganisms consume more oxygen, so the value of $$\text{BOD}$$ increases. Conversely, if the water contains very little organic impurity, microorganisms need only a small amount of oxygen, so the value of $$\text{BOD}$$ will be low.

Mathematically we can say

$$\text{Organic pollution} \propto \text{BOD}$$

That single proportionality is enough to compare the four values given. Lower $$\text{BOD}$$ means lower organic pollution, and therefore the water is cleaner.

The four values are $$11\ \text{ppm},\; 15\ \text{ppm},\; 3\ \text{ppm},\; 21\ \text{ppm}$$. Among these, $$3\ \text{ppm}$$ is clearly the smallest.

Because $$3\ \text{ppm}$$ is the minimum value, it represents the least oxygen required by microorganisms, indicating the smallest amount of biodegradable organic matter present.

Therefore, the sample having $$\text{BOD}=3\ \text{ppm}$$ will be the cleanest.

Hence, the correct answer is Option C.