Miscellaneous - Previous Year IPM/BBA Questions
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In a class, 60% and 68% of students passed their Physics and Mathematics examinations respectively. Then atleast ________ percentage of students passed both their Physics and Mathematics examinations.
Answer: 28
Text Explanation :
Let the percentage of students who passed in both the subjects is 'x' and those who failed in both the subjects is 'n'.
Now, P ∪ M = P + M - P ∩ M
⇒ 100 - n = 60 + 68 - x
⇒ x = n + 28
x will be least when n is least. Least value of n can be 0, hence least value of x = 28
Hence, 28.
Workspace:
Out of 80 students who appeared for the school exams in Mathematics (M), Physics (P) and Chemistry (C), 50 passed M , 30 passed P and 40 passed C. At most 20 students passed M and P at most 20 students passed P and C and at most 20 students passed C and M. The maximum number of students who could have passed all three exams is __________.
Answer: 20
Text Explanation :
To maximise the number of students who passed in all the three exams we will assume that no one failed in all the three exams.
∴ M ∪ P ∪ C = M + P + C - M ∩ P - P ∩ C - C ∩ M + M ∩ P ∩ C
⇒ M ∪ P ∪ C - (M + P + C) + M ∩ P + P ∩ C + C ∩ M = M ∩ P ∩ C
To maximise the number of students who passed in all the three exams we need to maximise M ∩ P and P ∩ C and C ∩ M.
Maximum value of M ∩ P =20, that of P ∩ C =20 and that of C ∩ M = 20
∴ 80 - (50 + 30 + 40) + 20 + 20 + 20 + M ∩ P ∩ C
⇒ 20 = M ∩ P ∩ C
Hence, 20.
Workspace:
In a school 70% of the boys like cricket and 50% like football. If x% like both Cricket and Football, then
- (a)
20 ≤ x ≤ 50
- (b)
x ≤ 20
- (c)
x ≥ 50
- (d)
10 ≤ x ≤ 70
Answer: Option A
Text Explanation :
Workspace:
In a class of 65 students 40 like cricket, 25 like football and 20 like hockey. 10 students like both cricket and football, 8 students like football and hockey and 5 students like all three sports. If all the students like at least one sport, then the number of students who like both cricket and hockey is
- (a)
7
- (b)
8
- (c)
10
- (d)
12
Answer: Option A
Text Explanation :
Workspace: