In a class of 35 students, 18 read mathematics, 17 read physics and 4 do non of the subjects. Find how many students read
i. both mathematics and physics
ii. Only physics
i. To find out how many students read both mathematics and physics, we need to subtract the number of students who read neither subject from the total number of students:
Total number of students = 35
Number of students who read neither subject = 4
So, the number of students who read either mathematics or physics (or both) = 35 - 4 = 31
Now, we know that 18 students read mathematics and 17 students read physics. However, some of these students may be counted twice if they read both subjects. To find out how many students read both subjects, we can use the formula:
Number of students who read both = Total number of students who read mathematics + Total number of students who read physics - Total number of students who read either subject
Number of students who read both = 18 + 17 - 31 = 4
Therefore, 4 students read both mathematics and physics.
ii. To find out how many students read only physics, we need to subtract the number of students who read both mathematics and physics and the number of students who read neither subject from the total number of students who read physics:
Number of students who read physics = 17
Number of students who read both mathematics and physics = 4
Number of students who read neither subject = 4
Number of students who read only physics = 17 - 4 - 4 = 9
Therefore, 9 students read only physics.
To find the number of students who read both mathematics and physics, you can subtract the students who do not read any subject from the total number of students.
Given that there are 4 students who do not read any subject, the total number of students who read either mathematics or physics is:
Total = Total students - Students not reading any subject
Total = 35 - 4
Total = 31
Now, to find the number of students who read both mathematics and physics, you can add the number of students who read mathematics and the number of students who read physics, and then subtract the total number of students:
i. Students reading both mathematics and physics = Students reading mathematics + Students reading physics - Total students
i. = 18 + 17 - 31
i. = 35 - 31
i. = 4
Therefore, 4 students read both mathematics and physics.
To find the number of students who only read physics, you can subtract the number of students who read both mathematics and physics from the number of students who read physics:
ii. Students reading only physics = Students reading physics - Students reading both mathematics and physics
ii. = 17 - 4
ii. = 13
Therefore, 13 students only read physics.