In 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?
In 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? Correct Answer 34
Given:
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
Students studying only maths and physics =
(M ⋂ P) - (M ⋂ P ⋂ C) = 16 - 5 = 11 Students studying only maths and chemistry = (M ⋂ C) - (M ⋂ P ⋂ C) = 17 - 5 = 12 Students studying only chemistry and physics = (C ⋂ P) - (M ⋂ P ⋂ C) = 16 - 5 = 11Total students learning two subjects = 11 + 12 + 11 = 34
∴ The correct choice will be option 4.
