In an examination involving 30 candidates,31 passed mathematics,29 passed physics,while 3 failed both subjects. How many candidates passed (a)both subject,(b)physics only.

Answer 1

We can use a Venn diagram to solve this problem. Let the circle on the left represent the mathematics students, the circle on the right represent the physics students, and the overlapping region represent those who passed both subjects.

From the information given, we know that:

- 31 students passed mathematics, so the left circle has a total of 31 students.
- 29 students passed physics, so the right circle has a total of 29 students.
- 3 students failed both subjects, so the overlapping region has 3 students.

To find the number of students who passed both subjects, we subtract the number who failed both subjects from the total number of students:

Total students = 30
Failed both = 3
Passed at least one subject = 30 - 3 = 27
Passed both = 27 - 29 (passed physics only) = 2

Therefore, 2 students passed both mathematics and physics.

To find the number of students who passed physics only, we subtract the number who passed both subjects and the number who failed both subjects from the total number of students who passed physics:

Total passed physics = 29
Failed both = 3
Passed both = 2
Passed physics only = 29 - 2 - 3 = 24

Therefore, 24 students passed physics only.