Question
Download Solution PDF200 students appeared in a specific examination. There were 80 students who failed in Mathematics. 160 students passed in Physics. 30 students failed in Chemistry. 30 students failed in Mathematics and Physics. 15 students failed in Mathematics and Chemistry. 10 students failed in Physics and Chemistry. 100 students passed in all three subjects.
How many students failed in only one subject?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept used:
n(A U B U C) = n(A) + n (B) + n(c) - n(A ∩ B) - n(B ∩ C) - n(C ∩ A) + n(A ∩ B ∩ C)
Where, n(A U B U C) = no of students failed in all subject
n(A ∩ B ∩ C) = number of total students failed
Calculation:
Total students pass = 100
So, total students fail = 200 - 100 = 100
Students failed in Physics = 200 - 160 = 40
Now,
100 = 80 + 40 + 30 - (15 + 30 + 10) + students failed in all subjects
⇒ students failed in all subjects = 100 - 150 + 55
⇒ students failed in all subjects = 155 - 150 = 5
Again,
Failed in only (M, P) = 30 - 5 = 25
Failed in only (P, C) = 10 - 5 = 5
Failed in only (C, M) = 15 - 5 = 10
So,
Failed in only maths = 80 - (10 + 5 + 25) = 80 - 40 = 40
Failed in only physics = 40 - (25 + 5 + 5) = 40 - 35 = 5
Failed in only chemistry = 30 - (10 + 5 + 5) = 30 - 20 = 10
Thus, total students failed in only one subject = 40 + 5 + 10 = 55
∴ The correct answer is option (2).
Last updated on Jun 2, 2025
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