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In a survey of 200 students of a higher secondary school, it was found that 120 studied Mathematics, 90 studied Physics, 70 studied Chemistry, 40 studied Mathematics and Physics, 30 studied Physics and Chemistry, 50 studied Chemistry and Mathematics and 20 studied none of these subjects. Find the number of students who studied all the three subjects.
- a)10
- b)20
- c)0
- d)40
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In a survey of 200 students of a higher secondary school, it was found...
Given:
Total number of students surveyed = 200
Number of students who studied Mathematics = 120
Number of students who studied Physics = 90
Number of students who studied Chemistry = 70
Number of students who studied Mathematics and Physics = 40
Number of students who studied Physics and Chemistry = 30
Number of students who studied Chemistry and Mathematics = 50
Number of students who studied none of the subjects = 20
To Find: Number of students who studied all the three subjects.
Solution:
Let us start by drawing a Venn diagram to represent the given information.
From the given information, we can fill in the following information in the Venn diagram:
- Number of students who studied Mathematics only = 120 - 40 - 50 + x = 30 + x
- Number of students who studied Physics only = 90 - 40 - 30 + x = 20 + x
- Number of students who studied Chemistry only = 70 - 30 - 50 + x = 10 + x
- Number of students who studied Mathematics and Physics only = 0 (since all of them studied Mathematics and Physics)
- Number of students who studied Physics and Chemistry only = 0 (since all of them studied Mathematics and Physics)
- Number of students who studied Chemistry and Mathematics only = 0 (since all of them studied Mathematics and Physics)
- Number of students who studied all the three subjects = x
Total number of students who studied at least one of the subjects =
Number of students who studied Mathematics + Number of students who studied Physics + Number of students who studied Chemistry - Number of students who studied Mathematics and Physics - Number of students who studied Physics and Chemistry - Number of students who studied Chemistry and Mathematics + Number of students who studied all the three subjects
= 120 + 90 + 70 - 40 - 30 - 50 + x
= 160 + x
From the given information, we know that 20 students studied none of the subjects. Hence,
Total number of students surveyed = Number of students who studied at least one of the subjects + Number of students who studied none of the subjects
200 = 160 + x + 20
x = 20
Hence, the number of students who studied all the three subjects is 20.
Answer: Option B.
Total number of students surveyed = 200
Number of students who studied Mathematics = 120
Number of students who studied Physics = 90
Number of students who studied Chemistry = 70
Number of students who studied Mathematics and Physics = 40
Number of students who studied Physics and Chemistry = 30
Number of students who studied Chemistry and Mathematics = 50
Number of students who studied none of the subjects = 20
To Find: Number of students who studied all the three subjects.
Solution:
Let us start by drawing a Venn diagram to represent the given information.
From the given information, we can fill in the following information in the Venn diagram:
- Number of students who studied Mathematics only = 120 - 40 - 50 + x = 30 + x
- Number of students who studied Physics only = 90 - 40 - 30 + x = 20 + x
- Number of students who studied Chemistry only = 70 - 30 - 50 + x = 10 + x
- Number of students who studied Mathematics and Physics only = 0 (since all of them studied Mathematics and Physics)
- Number of students who studied Physics and Chemistry only = 0 (since all of them studied Mathematics and Physics)
- Number of students who studied Chemistry and Mathematics only = 0 (since all of them studied Mathematics and Physics)
- Number of students who studied all the three subjects = x
Total number of students who studied at least one of the subjects =
Number of students who studied Mathematics + Number of students who studied Physics + Number of students who studied Chemistry - Number of students who studied Mathematics and Physics - Number of students who studied Physics and Chemistry - Number of students who studied Chemistry and Mathematics + Number of students who studied all the three subjects
= 120 + 90 + 70 - 40 - 30 - 50 + x
= 160 + x
From the given information, we know that 20 students studied none of the subjects. Hence,
Total number of students surveyed = Number of students who studied at least one of the subjects + Number of students who studied none of the subjects
200 = 160 + x + 20
x = 20
Hence, the number of students who studied all the three subjects is 20.
Answer: Option B.
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Community Answer
In a survey of 200 students of a higher secondary school, it was found...
According to the question we get
n(M P C) = 200 - 20 = 180
or, n(M) = 120, n(P) = 90 and n(C) = 70
or, n(M P) = 40
or, n(P C) = 30
or, n(C M) = 50
or, n(M P C) = n(M) + n(P) + n(C) - n(M P) - n(P C) - n(C M) + n(M P C)
or, 180 = 120 + 90 + 70 - 40 - 30 - 50 + n(M P C)
or, 180 = 280 - 120 + n(M P C)
Hence, n(M P C) = 20
n(M P C) = 200 - 20 = 180
or, n(M) = 120, n(P) = 90 and n(C) = 70
or, n(M P) = 40
or, n(P C) = 30
or, n(C M) = 50
or, n(M P C) = n(M) + n(P) + n(C) - n(M P) - n(P C) - n(C M) + n(M P C)
or, 180 = 120 + 90 + 70 - 40 - 30 - 50 + n(M P C)
or, 180 = 280 - 120 + n(M P C)
Hence, n(M P C) = 20
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In a survey of 200 students of a higher secondary school, it was found that 120 studied Mathematics, 90 studied Physics, 70 studied Chemistry, 40 studied Mathematics and Physics, 30 studied Physics and Chemistry, 50 studied Chemistry and Mathematics and 20 studied none of these subjects. Find the number of students who studied all the three subjects.a)10b)20c)0d)40Correct answer is option 'B'. Can you explain this answer?
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