To find the total number of students who appeared in the examination, we can use the concept of set theory and Venn diagrams.
Let's assume the total number of students who appeared in the examination is represented by the variable 'x'.
According to the given information:
- 80% of students passed in Physics, which means 80% of 'x' students passed in Physics.
- 70% of students passed in Chemistry, which means 70% of 'x' students passed in Chemistry.
- 15% of students failed in both the subjects, which means 15% of 'x' students failed in both Physics and Chemistry.
- 390 students passed in both the subjects.
Using this information, we can create an equation based on the principle of inclusion-exclusion:
(Number of students who passed in Physics) + (Number of students who passed in Chemistry) - (Number of students who passed in both) + (Number of students who failed in both) = Total number of students
Let's solve this equation to find the value of 'x':
(80% of x) + (70% of x) - (390) + (15% of x) = x
Simplifying the equation:
0.80x + 0.70x - 390 + 0.15x = x
1.65x - 390 = x
0.65x = 390
x = 390 / 0.65
x = 600
Therefore, the total number of students who appeared in the examination is 600.
Hence, the correct answer is option C) 600.