Question

In a college, graduate students got distinctions of three subjects i.e. P, Q and R. Subject P is taken by 26
percent students, 25 percent students took subject Q and subject R is taken by 14 percent. Subject P and a
are taken by 11 percent while subject Q and R are taken by 10 percent. Subject R and P are taken by 9
percent while subject R alone is not taken by any student.
What is the percentage of students who taken subject P and Q but not subject R?
4
8
10
6​

Answer 1

Given : Subject P is taken by 26  percent students, 25 percent students took subject Q and subject R is taken by 14 percent. Subject P and a

are taken by 11 percent while subject Q and R are taken by 10 percent. Subject R and P are taken by 9  percent while subject R alone is not taken by any student.

To Find : What is the percentage of students who taken subject P and Q but not subject R

Solution:

P = 26

Q = 25

R = 14

P∩Q = 11

R∩Q = 10

R ∩ P = 9

R alone = R - R ∩ P - R∩Q  + R∩P∩Q    = 0

=> 14  - 9 - 10  + R∩P∩Q    = 0

=> R∩P∩Q = 5

taken subject P and Q but not subject R

= P∩Q -  R∩P∩Q

= 11 - 5

= 6

6 percentage of students who taken subject P and Q but not subject R

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