Question

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 m and n respectively be the least and the most number of students who studied all the three subjects. Then m + n is equal to _______.

Answer 1

Correct answer: 45

\(125 \leq \mathrm{m}+90-\mathrm{x} \leq 130\)

\(85 \leq \mathrm{P}+70-\mathrm{x} \leq 95\)

\(75 \leq \mathrm{C}+80-\mathrm{x} \leq 90\)

\(\mathrm{m}+\mathrm{P}+\mathrm{C}+120-2 \mathrm{x}=210\)

\(\Rightarrow 15 \leq \mathrm{x} \leq 45\ \& \ 30-\mathrm{x} \geq 0\)

\(\Rightarrow 15 \leq \mathrm{x} \leq 30\)

\(30+15=45\)