200 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?

Question

Question

This question was previously asked in

RRC Group D Previous Paper 50 (Held On: 14 Dec 2018 Shift 2)

Answer 1

Concept 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:

Sourav SSC 07-02-25 Amit raj 10.

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).

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