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 none of these subjects. Find the number of students who study only maths

Answer 1

your answer is 120 students likeing maths

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.