Question

In a survey of 200 students of a school, it was found that 120 study mathematics, 90 study physics and 70 study chemistry, 40 study Mathematics and Physics, 30 study Physics and Chemistry, 50 study Chemistry and Mathematics and 20 study none of these.Find the number of students
→ only one subject
→ at most one subject
→ at least one subject.

plz answer me fast!

Answer 1

Answer:

Total no of students=420

Most of the children study mathematics

and least one is physics

Answer 2

Answer:

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Explanation:

Let M, P and C denote the students studying Mathematics, Physics and Chemistry

And U represents total students

So, n(U)=200,

n(M)=120,n(P)=90

n(C)=70,n(M∩P)=40,n(P∩C)=30

n(M∩C)=50,n(M∪P∪C)′=20

∴n(M∪P∪C)′=n(U)−n(M∪P∪C)

⇒20=200−n(M∪P∪C)

⇒n(M∪P∪C)=180

⇒n(M∪P∪C)=n(M)+n(P)+n(C)

−n(M∩P)−n(P∩C)−n(C∩M)+n(C∩M∩P)

∴180=120+90+70−40−30−50+n(C∩M∩P)

⇒180=280−120+n(C∩M∩P)

⇒n(P∩C∩M)=300−280=20

Hence, the number of students studying all three subjects is 20.