89 students of class 8 appeared for a combined test in maths and physics . If 62 students passed in both 4 failed in maths and physics and 7 failed in maths only use Venn diagram to find 1 failed in physics 2 passed in maths 3 passed in physics
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Answered by
4
Total number of students appeared = 89
total passed students = 62
students failed in maths and physics = 4
Students failed in maths = 7
Thus clearly,
total number of failed students = 89 - 62 = 27
Thus
Students failed in physics = 27 - 7 = 20
Students passed in maths = 27 - 7 = 20 + 62 = 82
Students passed in physics = 7 + 62 = 69
total passed students = 62
students failed in maths and physics = 4
Students failed in maths = 7
Thus clearly,
total number of failed students = 89 - 62 = 27
Thus
Students failed in physics = 27 - 7 = 20
Students passed in maths = 27 - 7 = 20 + 62 = 82
Students passed in physics = 7 + 62 = 69
Answered by
2
Solution :-
Let P denote the set of students who passed in Physics, and M denote the set of students who passed in Mathematics. This information is presented in a Venn Diagram. The image is attached.
The number of students passed in Mathematics only is represented by 'a' (i.e. failed in physics)
The number of students passes in Physics only is represented by 'c' (i.e. failed in Mathematics)
The number of students passed in both Physics and Mathematics is represented by 'b'
The number of students failed in both subjects is represented by 'd'
Given that number of students who passed in both subjects = 'b' = 62
Given that 4 failed in Mathematics and Physics = 'd' = 4
Given that 7 students failed in Mathematics. The students who failed in Mathematics represented by the region 'c' and 'd'
⇒ c + d = 7
⇒ c = 7 - d
⇒ c = 7 - 4
c = 3
Given that 89 students appeared in the test. The students appeared in the test are represented by 'a', 'b', 'c' and 'd'
a + b + c + d = 89
a + 62 + 3 + 4 = 89
a + 89 - 69
a = 20
So,
1) The number of students who failed in Physics only are represented by 'a' = 20
2) The number of students who passed in Mathematics are represented by 'a' and 'b'
= a + b
= 20 + 62
= 82
3) The number of students who passed in Physics is represented by 'c' and 'b'
= c + b
= 3 + 62
= 65
Answer.
Let P denote the set of students who passed in Physics, and M denote the set of students who passed in Mathematics. This information is presented in a Venn Diagram. The image is attached.
The number of students passed in Mathematics only is represented by 'a' (i.e. failed in physics)
The number of students passes in Physics only is represented by 'c' (i.e. failed in Mathematics)
The number of students passed in both Physics and Mathematics is represented by 'b'
The number of students failed in both subjects is represented by 'd'
Given that number of students who passed in both subjects = 'b' = 62
Given that 4 failed in Mathematics and Physics = 'd' = 4
Given that 7 students failed in Mathematics. The students who failed in Mathematics represented by the region 'c' and 'd'
⇒ c + d = 7
⇒ c = 7 - d
⇒ c = 7 - 4
c = 3
Given that 89 students appeared in the test. The students appeared in the test are represented by 'a', 'b', 'c' and 'd'
a + b + c + d = 89
a + 62 + 3 + 4 = 89
a + 89 - 69
a = 20
So,
1) The number of students who failed in Physics only are represented by 'a' = 20
2) The number of students who passed in Mathematics are represented by 'a' and 'b'
= a + b
= 20 + 62
= 82
3) The number of students who passed in Physics is represented by 'c' and 'b'
= c + b
= 3 + 62
= 65
Answer.
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