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Question

# In a certain class, one-third of the students were absent. Half of the total strength attended the Maths test and one-fourth of the total strength attended the Physics test. If 6 students attended both the tests and every student who was present attended at least one of the two tests, then how many students were absent on that day ?

A
16
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B
18
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C
24
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D
32
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Solution

## The correct option is C 24 Let the total no. of students are x . No. of students which were absent =x3 . No. of students which were present =2x3 Now, No. of dtudents who gove maths test =x2 No. of students who gave physics test: x4 No. of students who gave both test =6 A denotes no. of students whogawe maths test B denotes no. of students who gave physics test n(A)=x2n(B)=x4n(A∩B)=6 n(A∪B)= no. of students which were present n(A∪B)=n(A)+n(B)−n(A∩B)2x3=x2+x4−6x=72 No. of students which are absent =723=24

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