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$P, Q, R$ and $S$ are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within $24$ hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below: A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?

1. $P$
2. $Q$
3. $R$
4. $S$

As per the question, it is quite clear that the danger of a microbe to human being will be directly proportional to potency and growth. At the same time it is inversely proportional to toxicity, defined as( more dangerous will a microbe be if lesser of its milligram is required).

So, $\text{Level Of Danger (D)} \propto \text{Growth (G)} \propto \text{Potency (P) }\dfrac{1}{\propto} \text{ Toxicity (T)}$

$D = \dfrac{KGP}{T}$

where K is constant of proportionality.

So level of danger will be maximum for $S.$

Given by,

$D_S =\dfrac{0.8\times \large\pi(10)^{2}}{200}$

$\qquad= 1.256$

Similar calculations for $D{_P} , D{_Q} , D{_R}$ can be done. Which will consequently lead to $D{_S}$ being the most dangerous and hence will be targeted first.

this apparoch worked due to fact that here data can be easily distinguished. But if data have been more compact or less degree of change then then accurate calculation would have been required.

The fact mentioned in the answer by @ is wrong. Sir, you have mentioned that Level Of Danger (D)∝Growth (G)∝Potency (P) 1∝ Toxicity (T)   whereas in the question its mentioned that Level Of Danger (D)∝Growth (G)∝Potency (P) ∝ Toxicity (T)   which implies

Level Of Danger (D)= constant * Growth (G) * Potency (P) * Toxicity (T)

Hence accordingly, answer should be option A i.e. P.

Note- it can also be seen in the graph that although S has high potency but its toxicity and growth level is very low. Whereas in P, its growth and toxicity is high. Hence option A.

Please see the y-axis label of the graph.
danger is inversely proportional to toxicity as the most dangerous would be the one which require less milligram to destroy half of body mass

SO, danger = (K * potency * growth)/toxicity

answer will be S

SO OPTION (D)
by

Tnx for the answer....As the question says- The danger to human beings varies proportionately with the toxicity, potency and growth...nothing about direct proportionality

Hence, Toxicity is considered as inversely proportional as given in the graph.

So where it is mentioned that toxicity has to be inversely proportional

They said varies proportionally but not is proportional to. To be frank I don't understand why the paper setters care so much about skills in interpreting the question rather than the analytical and reasoning skills of the student. I would have surely considered it as directly proportional the moment I see varies proportionally.

if your see the definition of toxicity  in the graph you would easily find that  lesser the milligram  more the  toxicity and hence more  dangerous the microbe will be.So due high potency and less  toxicity  S would be the better choice among all.