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 mo

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 ______

Question diagram: In a survey of 220 students of a higher secondary school, it

Answer:

45.00

Solution:

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

TestHub · Accepted Answer

​ 125 ≤ m + 90 − x ≤ 130 85 ≤ P + 70 − x ≤ 95 75 ≤ C + 80 − x ≤ 90 m + P + C + 120 − 2 x = 210 ⇒ 15 ≤ x ≤ 45&30 − x ≥ 0 ⇒ 15 ≤ x ≤ 30 30 + 15 = 45 ​

Mathematics - Sets and Relations Question with Solution | TestHub

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