Question

In a class of 180 students,1/4 members study Physics and Chemistry,1/4 members study Maths. 20% of those who read Maths also study Physics and Chemistry. About 20 percent of those who study physics and chemistry study maths. 30 percent of all readers also play games? How many people read Maths, but not Physics and Chemistry
​

Answer 1

Answer:

Correct option is

B

20

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.

Answer 2

Answer:

36

Step-by-step explanation:

Total students = 180

No. of students studying Maths = 1/4 of 180 = 180/4 = 45

% of Maths students studying physics and chemistry

= 20% of students studying Maths = 20% of 45 = 9

Mo. of students who read Maths but not Physics and Chemistry = 45–9 = 36