Question

6. Out of 300 students in a class, 60% students study Physics, 35% students Chemistry and 20% students do not study both of the subjects. i. How many students study both subjects? ii. How many students study Physics only? iii. How many students study Chemistry only? iv. What is the number of students who study only one subject? Find it.​

Answer 1

Answer:

Correct option is

B

10 students study each of Mathematics, Physics and Chemistry

C

70 students study either Mathematics or Chemistry

D

35 students study Mathematics along with either Physics or Chemistry

Given there are 100 students in a class,

let M be the set of people who study mathematics,∴n(M)=60,

let P be the set of people who study physics, ∴n(P)=45,

let C be the set of people who study chemistry, ∴n(C)=35,

Also given that n(M∩P)=20, n(P∩C)=15 and n(M∩C)=25

10 students study none of these subjects

∴100−n(M∪P∪C)=10

⇒n(M∪P∪C)=90

n(M∪P∪C)=n(M)+n(P)+n(C)−n(M∩P)−n(P∩C)−n(M∩C)+n(M∩P∩C)

⇒90=60+45+35−20−15−25+n(M∩P∩C)

⇒n(M∩P∩C)=10

So, option B is correct.

Now, n(M∪C)=n(M)+n(C)−n(M∩C)=60+35−25=70

So, option C is correct.

Also, n(P∪C)=n(P)+n(C)−n(P∩C)=45+35−15=65

To find n(M∩(P∪C))

n(M∩(P∪C))=n(M)+n(P∪C)−n(M∪P∪C)=60+65−90=35

Hence, option B,C and D are correct

Step-by-step explanation:

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