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Out of a group of 20 teachers in a school, 10 teach Mathematics, 9 teach Physics and 7 teach Chemistry, 4 teach both Mathematics and Physics, but none teach both mathematics and Chemistry. What is the number of teachers who teach both Chemistry and Physics ?
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Out of a group of 20 teachers in a school, 10 teach Mathematics, 9 tea...
Given:
- Total number of teachers in the school = 20
- Number of teachers who teach Mathematics = 10
- Number of teachers who teach Physics = 9
- Number of teachers who teach Chemistry = 7
- Number of teachers who teach both Mathematics and Physics = 4
- None of the teachers teach both Mathematics and Chemistry
To find:
- The number of teachers who teach both Chemistry and Physics
Solution:
Let's start by drawing a Venn diagram with three overlapping circles representing Mathematics, Physics and Chemistry.
From the given information, we know that:
- The total number of teachers = 20
- Number of teachers who teach Mathematics = 10
- Number of teachers who teach Physics = 9
- Number of teachers who teach Chemistry = 7
- Number of teachers who teach both Mathematics and Physics = 4
We can use this information to fill in the Venn diagram as follows:
- The number of teachers who teach Mathematics only = 10 - 4 = 6
- The number of teachers who teach Physics only = 9 - 4 = 5
- The number of teachers who teach Chemistry only = 7 - x (where x is the number of teachers who teach both Chemistry and Physics)
We also know that none of the teachers teach both Mathematics and Chemistry. Therefore, the overlap between Mathematics and Chemistry is 0.
Now, we can use the principle of inclusion-exclusion to find x, the number of teachers who teach both Chemistry and Physics.
- Total number of teachers who teach Chemistry or Physics = (6 + 4 + x) + (5 + 4 + x) + (7 - x) = 26
- Total number of teachers in the school = 20
We have counted the teachers who teach both Chemistry and Physics twice, so we need to subtract them once to get the total number of teachers who teach Chemistry or Physics.
- Total number of teachers who teach Chemistry or Physics = 26 - x
Now we can use the formula:
Total number of teachers = Number of teachers who teach Mathematics only + Number of teachers who teach Physics only + Number of teachers who teach Chemistry only + Number of teachers who teach both Chemistry and Physics
Substituting the values we know, we get:
20 = 6 + 5 + (7 - x) + 4 + x
Simplifying and solving for x, we get:
x = 2
Therefore, the number of teachers who teach both Chemistry and Physics is 2. So the correct answer is option B.
Final Answer: 2 teachers teach both Chemistry and Physics.
- Total number of teachers in the school = 20
- Number of teachers who teach Mathematics = 10
- Number of teachers who teach Physics = 9
- Number of teachers who teach Chemistry = 7
- Number of teachers who teach both Mathematics and Physics = 4
- None of the teachers teach both Mathematics and Chemistry
To find:
- The number of teachers who teach both Chemistry and Physics
Solution:
Let's start by drawing a Venn diagram with three overlapping circles representing Mathematics, Physics and Chemistry.
From the given information, we know that:
- The total number of teachers = 20
- Number of teachers who teach Mathematics = 10
- Number of teachers who teach Physics = 9
- Number of teachers who teach Chemistry = 7
- Number of teachers who teach both Mathematics and Physics = 4
We can use this information to fill in the Venn diagram as follows:
- The number of teachers who teach Mathematics only = 10 - 4 = 6
- The number of teachers who teach Physics only = 9 - 4 = 5
- The number of teachers who teach Chemistry only = 7 - x (where x is the number of teachers who teach both Chemistry and Physics)
We also know that none of the teachers teach both Mathematics and Chemistry. Therefore, the overlap between Mathematics and Chemistry is 0.
Now, we can use the principle of inclusion-exclusion to find x, the number of teachers who teach both Chemistry and Physics.
- Total number of teachers who teach Chemistry or Physics = (6 + 4 + x) + (5 + 4 + x) + (7 - x) = 26
- Total number of teachers in the school = 20
We have counted the teachers who teach both Chemistry and Physics twice, so we need to subtract them once to get the total number of teachers who teach Chemistry or Physics.
- Total number of teachers who teach Chemistry or Physics = 26 - x
Now we can use the formula:
Total number of teachers = Number of teachers who teach Mathematics only + Number of teachers who teach Physics only + Number of teachers who teach Chemistry only + Number of teachers who teach both Chemistry and Physics
Substituting the values we know, we get:
20 = 6 + 5 + (7 - x) + 4 + x
Simplifying and solving for x, we get:
x = 2
Therefore, the number of teachers who teach both Chemistry and Physics is 2. So the correct answer is option B.
Final Answer: 2 teachers teach both Chemistry and Physics.
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Out of a group of 20 teachers in a school, 10 teach Mathematics, 9 teach Physics and 7 teach Chemistry, 4 teach both Mathematics and Physics, but none teach both mathematics and Chemistry. What is the number of teachers who teach both Chemistry and Physics ?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Out of a group of 20 teachers in a school, 10 teach Mathematics, 9 teach Physics and 7 teach Chemistry, 4 teach both Mathematics and Physics, but none teach both mathematics and Chemistry. What is the number of teachers who teach both Chemistry and Physics ?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Out of a group of 20 teachers in a school, 10 teach Mathematics, 9 teach Physics and 7 teach Chemistry, 4 teach both Mathematics and Physics, but none teach both mathematics and Chemistry. What is the number of teachers who teach both Chemistry and Physics ?a)1b)2c)3d)4Correct answer is option 'B'. Can you explain this answer?.
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