$20$ teachers of a school teach either mathematics or physics. $12$ of them teach mathematics while $4$ teach both the subjects. Then number of teacher teaching only physics is

12

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8

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6

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none of these

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Solution

The correct option is A $12$
Total number of teachers $= 20$

Let
$A=no. of teacher teaches maths=12$
$B=no. of teacher teaches physics=n$
$C=no. of teacher teaches maths or physics=4$

Hence,
$n (A \cup B) = n (A) + n (B) - n (A \cap B)$
$⟹ n (B) = 20 - 12 + 4 = 12$

So, the number of teachers teaches physics only is $12$ .

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20 teachers of a school teach either mathematics or physics. 12 of them teach mathematics while 4 teach both the subjects. Then number of teacher teaching only physics is

The correct option is A 12Total number of teachers=20LetA=no. of teacher teaches maths=12B=no. of teacher teaches physics=nC=no. of teacher teaches maths or physics=4Hence,n(A∪B)=n(A)+n(B)−n(A∩B)⟹n(B)=20−12+4=12So, the number of teachers teaches physics only is 12.

$20$ teachers of a school teach either mathematics or physics. $12$ of them teach mathematics while $4$ teach both the subjects. Then number of teacher teaching only physics is