Answer:
Let's use a Venn diagram to solve this problem.
First, let's label the three regions of the Venn diagram: Computer only (C), Optional Maths only (M), and both Computer and Optional Maths (C ∩ M). We can also label the region outside the circles as neither Computer nor Optional Maths (N).
We know that 30% of the students like Computer only, which means that the percentage of students in region C is 30%. Similarly, 25% of the students like both Computer and Optional Maths, so the percentage of students in region C ∩ M is 25%.
We are also given that 5% of the students don't like either subject, so the percentage of students in region N is 5%.
Finally, we are told that 390 students like Optional Maths, which includes the students in regions M and C ∩ M. We don't know the percentage of students in region M, but we do know that the percentage of students in region C ∩ M is 25%.
Using this information, we can set up an equation to solve for the total number of students:
C + M + C ∩ M + N = 100%
Substituting the percentages we know, we get:
30% + M + 25% + 5% = 100%
Simplifying the equation, we get:
M = 40%
This means that 40% of the students like Optional Maths only, which is the percentage of students in region M.
Now we can use the fact that 390 students like Optional Maths to solve for the total number of students:
M + C ∩ M = 390
0.4T + 0.25T = 390
0.65T = 390
T = 600
Therefore, the total number of students is 600.