Water filled in two glasses A and B gave BOD values of 10 and 20, respectively. The correct statement regarding them is:

First, recall the definition: the Biological Oxygen Demand (BOD) of a water sample is the mass of dissolved oxygen (in milligrams per litre) that aerobic microorganisms need to oxidise the organic matter present in the water over a standard period (usually 5 days at 20 °C). In simple words, higher BOD means more biodegradable organic pollutants are present, so more oxygen is consumed and the water quality is poorer.

Mathematically we can write the direct proportionality

$$\text{Pollution level} \;\propto\; \text{BOD}$$

and the usual drinking-water guideline is

$$\text{BOD}_{\text{permissible}} < 5 \;\text{mg\,L}^{-1}.$$

Now, for the two glasses we have the numerical data

$$\text{BOD}_A = 10\;\text{mg\,L}^{-1}, \qquad \text{BOD}_B = 20\;\text{mg\,L}^{-1}.$$

Both of these individual values clearly violate the $$<5\;\text{mg\,L}^{-1}$$ criterion, so neither sample qualifies as potable (drinking) water. To compare their relative pollution levels, simply look at the difference:

$$\text{BOD}_B - \text{BOD}_A = 20 - 10 = 10\;\text{mg\,L}^{-1} > 0,$$

which shows $$\text{BOD}_B > \text{BOD}_A.$$ Because BOD is directly proportional to the concentration of organic pollutants, the larger value corresponds to the more polluted sample. Thus glass B, with the higher BOD of $$20\;\text{mg\,L}^{-1},$$ is more polluted than glass A.

Among the given options, the only statement that matches this conclusion is “B is more polluted than A.”

Hence, the correct answer is Option B.