"In a survey of 400 students of a college it was found that 240 study mathematics, 180 study Statistics and 140 study Accounts, 80 study mathematics and Statistics, 60 study Statistics and Accounts, 100 study Accounts and mathematics and 40 study none of these subjects. On the basis of this information answer the following questions."
1. Number of students studied accounts only
2. Number of students studied at least one of these subjects
3. Number of students studied all of these subjects
Answers
Answer:
1) Number of students studied accounts only = 20 students
2. Number of students studied at least one of these subjects = 360 students
3. Number of students studied all of these subjects = 40 students
Step-by-step explanation:
Number of students studied accounts only = 20 , Number of students studied at least one of these subjects= 360 & Number of students studied all of these subjects = 40
Step-by-step explanation:
Total Students T = 400
Study Mathematics M = 240
Study Statistics S = 180
Study Accounts A = 140
Study Mathematics & Statistics = M ∩ S = 80
Study Mathematics & Accounts = M ∩ A = 100
Study Accounts & Statistics = A ∩ S = 60
None of the Subjects N = 40
Study all three Subjects = M ∩ S ∩ A
T = M + S + A - M ∩ S - M ∩ A - A ∩ S + M ∩ S ∩ A + N
=> 400 = 240 + 180 + 140 - 80 - 100 - 60 + M ∩ S ∩ A + 40
=> M ∩ S ∩ A = 40
Number of students studied all of these subjects = 40
Number of students studied accounts only = A - M ∩ A - A ∩ S + M ∩ S ∩ A
= 140 - 100 - 60 + 40
= 20
Number of students studied accounts only = 20
Number of students studied at least one of these subjects= Total - None
= 400 - 40
= 360
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