Final answer:
By using a Venn Diagram and solving the system of equations, we find that 10 students appeared in all the subjects, 0 students in Hindi only, and the calculation for Commerce only suggests a negative number of students, indicating a possible error.
Step-by-step explanation:
To find the number of students who appeared in all subjects, in Hindi only, and in Commerce only using a Venn Diagram, we'll start by labeling three overlapping circles representing the subjects Economics, Hindi, and Commerce.
- 125 students appeared for Economics (E).
- 100 students appeared for Hindi (H).
- 145 students appeared for Commerce (C).
- 25 students appeared for Economics only (E only).
- 30 students appeared for both Economics and Hindi (E & H).
- 80 students appeared for both Economics and Commerce (E & C).
- 60 students appeared for both Hindi and Commerce (H & C).
Let's denote the students who appeared in all three subjects as x.
To calculate x, we add the numbers of students who appeared for both subjects and subtract the students who appeared only for one subject from the total number of students who appeared for that subject:
- For Economics (E): 125 = 25 (E only) + 30 (E & H) + 80 (E & C) - x
- For Hindi (H): 100 = x + 30 (E & H) + 60 (H & C)
- For Commerce (C): 145 = x + 80 (E & C) + 60 (H & C)
Using the equations, we can solve for x, which is the number of students who appeared in all subjects. We can then find the number who appeared in Hindi only and Commerce only.
By solving the equations:
- 125 = 25 + 30 + 80 - x
- 100 = x + 30 + 60
- 145 = x + 80 + 60
We have:
- x = 135 - 125 = 10 students appeared in all the subjects.
- For Hindi only: 100 = 10 + 30 + 60 = 0 students.
- For Commerce only: 145 = 10 + 80 + 60 = -5 students (which is not possible, indicating a possible error in the given data or the question).
Based on the pattern of data given, there seems to be an inconsistency that could suggest there is an error.