Question

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 students who studies all three subjects?
1. 5
2. 6
3. 7
4. 4

Answer 1

Correct Answer - Option 1 : 5

Given:

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.

Calculations:

Total number of students in all subjects(M ⋃ P ⋃ C) = 105  

Mathematics students M = 47

Physics students P = 50 

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 in all subjects are 5.

∴ The correct answer will be option 1.