Question

In a class of 60 students,27 study physics and 42 study maths and each person study at least one of the two subjects.How many students study both physics and maths?Answer is 9 but don't know how.or it is wrong question..?

Answer 1

Hey There,

We can solve this question by Set Theory.


Let Set A = Students who Study Physics

Set B = Students who Study Maths


We are given:
n(A) = 27

n(B) = 42


And Since total number of students is 60, we have:

$n(A \cup B) = 60$

We need $n(A\cap B)$


We know the identity:

$n(A \cup B) = n(A) + n(B) - n(A \cap B) \\ \\ \implies 60 = 27+42-n(A \cap B) \\ \\ \implies n(A \cap B) = 69-60 \\ \\ \implies \boxed{n(A \cap B)=9}$


Thus, 9 students study both Physics and Maths.



Hope it helps
Purva
Brainly Community