In the year 2019-20 the total number number of students 3 colleges a b...
**Explanation:**
To solve this problem, we need to break it down into different components and calculate each separately. Let's go step by step.
**Step 1: Number of Students in Each College**
Given that the ratio of students in colleges A, B, and C is 3:2:1, let's assume that the total number of students in these colleges is 6x.
So, the number of students in college A = 3x
The number of students in college B = 2x
The number of students in college C = x
**Step 2: Gender-wise Distribution**
The ratio of boys to girls in all the colleges is given as 3:2. Let's assume that the number of boys is 3y and the number of girls is 2y.
So, the number of boys in college A = (3/5) * (3x) = 9x/5
The number of girls in college A = (2/5) * (3x) = 6x/5
Similarly,
The number of boys in college B = (3/5) * (2x) = 6x/5
The number of girls in college B = (2/5) * (2x) = 4x/5
The number of boys in college C = (3/5) * (x) = 3x/5
The number of girls in college C = (2/5) * (x) = 2x/5
**Step 3: Facilities-wise Distribution**
The ratio of boys to girls in the facilities of arts, science, and commerce is given as 2:2:1. Let's assume that the number of boys in each facility is 2z, and the number of girls in each facility is 2z.
So, the number of boys in the arts facility = (2/5) * (9x/5) = 18x/25
The number of girls in the arts facility = (2/5) * (6x/5) = 12x/25
Similarly,
The number of boys in the science facility = (2/5) * (6x/5) = 12x/25
The number of girls in the science facility = (2/5) * (4x/5) = 8x/25
The number of boys in the commerce facility = (1/5) * (3x/5) = 3x/25
The number of girls in the commerce facility = (1/5) * (2x/5) = 2x/25
**Final Answer:**
Therefore, the final distribution of boys and girls in the facilities of arts, science, and commerce in colleges A, B, and C is as follows:
- Arts Facility: Boys - 18x/25, Girls - 12x/25
- Science Facility: Boys - 12x/25, Girls - 8x/25
- Commerce Facility: Boys - 3x/25, Girls - 2x/25
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