In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and Chemistry; 50 studied both Chemistry and…

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In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and Chemistry; 50 studied both Chemistry and Mathematics; 40 studied both Mathematics and Physics and 10 studied none of these subjects. Let $\mathrm{m}$ and $\mathrm{n}$ respectively be the least and the most number of students who studied all the three subjects. Then $\mathrm{m}+\mathrm{n}$ is equal to ______

Aicharya · Accepted Answer

$\begin{aligned} & 125 \leq \mathrm{m}+90-\mathrm{x} \leq 130 \\ & 85 \leq \mathrm{P}+70-\mathrm{x} \leq 95 \\ & 75 \leq \mathrm{C}+80-\mathrm{x} \leq 90 \\ & \mathrm{~m}+\mathrm{P}+\mathrm{C}+120-2 \mathrm{x}=210 \\ & \Rightarrow 15 \leq \mathrm{x} \leq 45 \& 30-\mathrm{x} \geq 0 \\ & \Rightarrow 15 \leq \mathrm{x} \leq 30 \\ & 30+15=45\end{aligned}$

In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130…

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