In a school, there are 20 teachers who teach mathematics or physics. O

1.	In a school, there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics, and 4 teach physics and mathematics. How many teach physics?
Answer» Here, we have, Since, teachers for teaching physics or math = 20 Teachers for teaching physics and math = 4 Teachers for teaching maths = 12 Suppose teachers who teach physics be ‘n (P)’ and for Maths be ‘n (M)’ Then, Since, teachers who teach for physics or math = n (P ∪ M) = 20 4 teachers who teach for physics and math = n (P ∩ M) = 4 12 teachers who teach for maths = n (M) = 12 As we know, n (P ∪ M) = n (M) + n (P) – n (P ∩ M) On substituting the values we get, 20 = 12 + n (P) – 4 20 = 8 + n (P) n (P) =12 Hence, there are 12 physics teachers.

In a school, there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics, and 4 teach physics and mathematics. How many teach physics?

Answer»

Here, we have,

Since, teachers for teaching physics or math = 20

Teachers for teaching physics and math = 4

Teachers for teaching maths = 12

Suppose teachers who teach physics be ‘n (P)’ and for Maths be ‘n (M)’

Then,

Since, teachers who teach for physics or math = n (P ∪ M) = 20

4 teachers who teach for physics and math = n (P ∩ M) = 4

12 teachers who teach for maths = n (M) = 12

As we know,

n (P ∪ M) = n (M) + n (P) – n (P ∩ M)

On substituting the values we get,

20 = 12 + n (P) – 4

20 = 8 + n (P)

n (P) =12

Hence, there are 12 physics teachers.