There are 900 students in a college, each belonging to one or more of the categories A, B, and C games. The ratio of students in only A, only B, and only C is $2 : 3 : 5$ respectively. The number of students in all three categories is 50\% of the number of students in only C. The sum of students who are in only B and C but not A, and those who are in only A and C but not B is 155. The number of students who are in A and B but not C is 30 less than the number of students who are in only B.

What is the ratio of the total number of students in category B to that in category C?

Question

There are 900 students in a college, each belonging to one or more of the categories A, B, and C games. The ratio of students in only A, only B, and only C is $2 : 3 : 5$ respectively. The number of students in all three categories is 50\% of the number of students in only C. The sum of students who are in only B and C but not A, and those who are in only A and C but not B is 155. The number of students who are in A and B but not C is 30 less than the number of students who are in only B.

What is the ratio of the total number of students in category B to that in category C?

Accepted Answer

**Solution:**

1. Let the number of students in only A, only B, and only C be $2x$, $3x$, and $5x$ respectively.

2. Total students are 900, so:
   $$2x + 3x + 5x + 	ext{(students in other overlapping categories)} = 900$$

3. Number of students in all three categories is 50\% of only C, so:
   $$	ext{All three} = \frac{50}{100} 	imes 5x = 2.5x$$

4. The sum of students in only B & C but not A and only A & C but not B is 155.

5. Students in A & B but not C are 30 less than only B, so:
   $$	ext{A & B not C} = 3x - 30$$

6. We have multiple unknowns for overlapping categories, but insufficient information to find exact values of $x$ or the overlapping groups.

7. Since the total number of students in category B and category C depends on these unknown overlaps, the ratio of total students in B to C cannot be determined with the given data.

**Answer:** Can't be determined

Answer

Answer

Answer

Answer