Q. 154.1( 42 Votes )
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 :
Given :
20 teachers teach physics or math.
4 teachers teach physics and math.
12 teach maths
Let us denote teachers who teach physics as n(P) and for Maths n(M).
Now ,
20 teachers teach physics or math = n(P ∪ M) = 20
4 teachers teach physics and math = n (P ∩ M) = 4
12 teach maths = n(M) =12
We know,
n (P ∪ M) = n(M) + n(P) – n (P ∩ M)
Substituting the values we get
20 = 12+n(P)–4
20 = 8+ n(P)
n(P) =12
∴ There are 12 physics teachers.
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