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In a class of 1000 students, 64% and 56% study Maths and Physics, respectively. Calculate how many students study both the subjects, given that each student studies at least one subject.
- a)80
- b)120
- c)200
- d)180
- e)250
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In a class of 1000 students, 64% and 56% study Maths and Physics, res...
To solve this problem, we can use the concept of overlapping sets.
Let's assume that the number of students who study both Maths and Physics is x.
Given that 64% of the students study Maths and 56% study Physics, we can calculate the number of students who study only Maths and only Physics as follows:
Number of students who study only Maths = 64% of 1000 = 0.64 * 1000 = 640
Number of students who study only Physics = 56% of 1000 = 0.56 * 1000 = 560
Now, since each student studies at least one subject, the total number of students who study either Maths or Physics is the sum of the number of students who study only Maths, only Physics, and both Maths and Physics:
Total number of students = Number of students who study only Maths + Number of students who study only Physics + Number of students who study both subjects
Given that the total number of students is 1000, we can write the equation as:
1000 = 640 + 560 + x
Simplifying the equation, we get:
1000 = 1200 + x
x = 1000 - 1200
x = -200
Since the number of students cannot be negative, we can conclude that there is an error in the given information.
However, if we assume that each student studies at least one subject, we can still calculate the number of students who study both subjects. In this case, the correct answer would be:
Number of students who study both subjects = Total number of students - Number of students who study only Maths - Number of students who study only Physics
Number of students who study both subjects = 1000 - 640 - 560
Number of students who study both subjects = 200
Let's assume that the number of students who study both Maths and Physics is x.
Given that 64% of the students study Maths and 56% study Physics, we can calculate the number of students who study only Maths and only Physics as follows:
Number of students who study only Maths = 64% of 1000 = 0.64 * 1000 = 640
Number of students who study only Physics = 56% of 1000 = 0.56 * 1000 = 560
Now, since each student studies at least one subject, the total number of students who study either Maths or Physics is the sum of the number of students who study only Maths, only Physics, and both Maths and Physics:
Total number of students = Number of students who study only Maths + Number of students who study only Physics + Number of students who study both subjects
Given that the total number of students is 1000, we can write the equation as:
1000 = 640 + 560 + x
Simplifying the equation, we get:
1000 = 1200 + x
x = 1000 - 1200
x = -200
Since the number of students cannot be negative, we can conclude that there is an error in the given information.
However, if we assume that each student studies at least one subject, we can still calculate the number of students who study both subjects. In this case, the correct answer would be:
Number of students who study both subjects = Total number of students - Number of students who study only Maths - Number of students who study only Physics
Number of students who study both subjects = 1000 - 640 - 560
Number of students who study both subjects = 200
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Community Answer
In a class of 1000 students, 64% and 56% study Maths and Physics, res...
Total number of students = 1000
Suppose, x students opt for both the subjects.
Number of students who study Maths = a + x = 640
Number of students who study Physics = b + x = 560
Here, a + x + b = 1000
∴ (640 - x) + x + (560 - x) = 1000
∴ x = 1200 - 1000 = 200
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In a class of 1000 students, 64% and 56% study Maths and Physics, respectively. Calculate how many students study both the subjects, given that each student studies at least one subject.a)80b)120c)200d)180e)250Correct answer is option 'C'. Can you explain this answer?
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