In a class of 55 students, the number of students studying different subjects is 23 in Mathematics and 24 in Physics, 19 in Chemistry, 12 in Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in Physics and Chemistry and 4 in all the three subjects. Which of the following is the number of students who have taken exactly one subject ?

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answer is D.

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Detailed Solution

Given , N=55, n(M)=23, n(P)=24, n(C)=19, n(M∩P)=12, n(P∩C)=7, n(M∩C)=9, n(M∩P∩C)=4
Now, number of students studying only Mathematics
n(M∩P′∩C′) = n(M)−n(M∩P)−n(M∩C)+n(M∩P∩C) (by Venn diagram)
⇒ 23−(12+9)+4 = 27−21 = 6
No. of students studying only physics is n(P)−[n(M∩P)+n(P∩C)]+n(M∩P∩C)
⇒ 24−(12+7)+4 = 28−19 = 9
No. of students studying only chemistry is n(C)−[n(M∩C)+n(P∩C)]+n(M∩P∩C)
⇒ 19−(9+7)+4 = 23−16 = 7
Therefore, the number of students who have taken exactly one subject is 6+9+7 = 22.
Hence, the correct option is Option 4.

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