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20 teachers of a school either teach mathematics or physics. 12 of them teach mathematics while 4 teach both the subjects. Then the number of teachers teaching physics only is
- a)12
- b)8
- c)16
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
20 teachers of a school either teach mathematics or physics. 12 of the...
Solution b
Let p be the set of teachers who teach physics.
M be the set of teachers who teaches the mathematics
Given n(M)=12
n(M∪P)=20
n(M∩P)=4
number of teachers who teaches physics n(P) =?
we know
n(M∪P) = n(M)+n(P)-n(M∩P)
20=12+n(P)-4
n(P)=12
Note in this problem it says only physics
number of teachers who teaches only physics=n(P)-n(M∩P)
=12-4
=8
Most Upvoted Answer
20 teachers of a school either teach mathematics or physics. 12 of the...
To solve this problem, we can use the principle of inclusion-exclusion.
Let's denote the number of teachers who teach only mathematics as M, the number of teachers who teach only physics as P, and the total number of teachers as T.
We know that 12 teachers teach mathematics, so M = 12.
We are also given that 4 teachers teach both mathematics and physics. This means that these 4 teachers are counted in both M and P. So, we can write the equation:
M + P - 4 = T
We are asked to find the number of teachers who teach physics only, which is P. To find P, we need to find T.
We know that the total number of teachers is 20, so T = 20.
Now we can substitute the values of M and T into the equation to find P:
12 + P - 4 = 20
Simplifying the equation, we get:
P = 20 - 12 + 4
P = 12
Therefore, the number of teachers who teach physics only is 12.
So, the correct answer is option B.
Let's denote the number of teachers who teach only mathematics as M, the number of teachers who teach only physics as P, and the total number of teachers as T.
We know that 12 teachers teach mathematics, so M = 12.
We are also given that 4 teachers teach both mathematics and physics. This means that these 4 teachers are counted in both M and P. So, we can write the equation:
M + P - 4 = T
We are asked to find the number of teachers who teach physics only, which is P. To find P, we need to find T.
We know that the total number of teachers is 20, so T = 20.
Now we can substitute the values of M and T into the equation to find P:
12 + P - 4 = 20
Simplifying the equation, we get:
P = 20 - 12 + 4
P = 12
Therefore, the number of teachers who teach physics only is 12.
So, the correct answer is option B.
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20 teachers of a school either teach mathematics or physics. 12 of them teach mathematics while 4 teach both the subjects. Then the number of teachers teaching physics only isa)12b)8c)16d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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