Answer:
Let's use a Venn diagram to solve the problem. We can start by drawing two intersecting circles to represent Science and Maths, respectively.
From the problem statement, we know that:
50 students like Science (this includes students who also like Maths)
35 students like Science but not Maths
5 students like neither Science nor Maths
To fill in the Venn diagram, we can start by placing the 35 students who like Science but not Maths in the part of the Science circle that does not overlap with the Maths circle. This leaves 15 students who like both Science and Maths (since 50 - 35 = 15).
We can then place the 5 students who like neither Science nor Maths outside of both circles.
Now we can answer the two questions:
(i) The number of students who like Maths is the total number of students in the Maths circle, which is the sum of the 15 who like both Science and Maths and the number of students who like Maths but not Science. Since we don't have that number directly, we can use the fact that the total number of students is 80, and we know that 50 like Science, so the remaining number (after subtracting the 5 who like neither) must be 30. Therefore, the number of students who like Maths is:
15 + (30 - 50) = 15 - 20 = -5
This doesn't make sense - it's impossible for a negative number of students to like Maths! We must have made a mistake somewhere.
Looking back at the Venn diagram, we see that the issue is that we can't place 35 students in the Science circle without overlapping with the Maths circle. In other words, some of the students who like Science but not Maths must also like Maths, since there are only 15 who like both. Let's adjust the diagram accordingly:
+---------+
| |
+----+ Science |
| | |
| +----+----+
| |
+------+ Maths |
| | |
| +---------+
|
| +---------------+
| | |
| | Neither |
| | |
+---+---------------+
| 5 |
Now we can see that the number of students who like Maths but not Science is 20 (since 35 - 15 = 20). Therefore, the number of students who like Maths is:
15 + 20 = 35
(ii) The number of students who like only one subject is the sum of the number of students who like Science but not Maths and the number of students who like Maths but not Science. From the adjusted Venn diagram, we see that those numbers are both 20. Therefore, the number of students who like only one subject is:
20 + 20 = 40
So, 35 students like Maths, and 40 students like only one subject.