Question
Download Solution PDFIn class of 105 students out of three subjects Maths, Physics, Chemistry each student studies at least one subject. In Maths 47, in Physics 50, and in Chemistry 52 students studies, 16 in Maths and Physics, 17 in Maths and Chemistry and 16 in Physics and Chemistry students both subjects.
What will be the number of those students who study only two subjects?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
In a class of 105 students out of three subjects Maths, Physics, Chemistry each student studies at least one subject. In Maths 47, in Physics 50, and in Chemistry 52 students studies, 16 in Maths and Physics, 17 in Maths and Chemistry and 16 in Physics and Chemistry students both subjects.
Calculations:
Total number of students M ⋃ P ⋃ C = 105
Only mathematics students M = 47
Only physics students P = 50
Only chemistry students C = 52
Mathematics and physic students M ⋂ P = 16
Mathematics and chemistry students M ⋂ C = 17
Physics and chemistry students P ⋂ C = 16
As we know that, M ⋃ P ⋃ C = M + P + C – (M ⋂ P) – (M ⋂ C) – (C ⋂ P) + (M ⋂ P ⋂ C)
105 = 47 + 50 + 52 – 16 – 17 – 16 + (M ⋂ P ⋂ C)
(M ⋂ P ⋂ C) = 105 – 100
(M ⋂ P ⋂ C) = 5
Total students learning two subjects = 11 + 12 + 11 = 34
Last updated on Jun 17, 2025
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