Question

in the examination 40% student failed in maths,30% failed in English, 50% failed in hindi, if 25% failed both math and English, 45% failed both in English and hindi, 65% student failed in hindi and math, 75% student failed in all three subject.Find passed precentage in all three subjects

Answer 1

Total% students failed in atleast 1 subject=40+30+50-(25+45+65)+75
=60%
40% passed in all 3

Answer 2

In the examination 40% student failed in maths,30% failed in English, 50% failed in hindi, if 25% failed both math and English, 45% failed both in English and hindi, 65% student failed in hindi and math, 75% student failed in all three subject.

The passed precentage in all three subjects is 40%

Step-by-step explanation:

Let

A : Set of students failed in Mathematics

B : Set of students failed in English

C : Set of students failed in Hindi

Then

n(A) = 40

n(B) = 30

n(C) = 50

$n(A\cap B)=25$

$n(B\cap C)=45$

$n(C\cap A)=65$

$n(A\cap B\cap C)=75$

Using

$\boxed{n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap B)-n(B\cap C)-n(C\cap A)+n(A\cap B\cap C)}$

$n(A\cup B\cup C)=40+30+50-25-45-65+75$

$\implies n(A\cup B\cup C)=60$

Therefore, the students that are failed in either of the subjects = 60%

Hence, students that ar passes in all the three subjects

= 100 - 60

= 40%

Hope this answer is helpful.

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