Directions (58-60) : Read the following information and answer the questions given below

In 10th class there are four sections namely A, B, C, and D. The ratio of total number of boys to total number of girls is 8:9. Ratio of boys to girls in school B is 1:3. The number of girls in school A and B is same. The number of boys in section C is 10 less than number of girls in section C and the number of girls in section D is 5 less than boys in section B. The number of girls in section C is 55 out of 225 total number of girls. The ratio of boys in section A and D is 5:8.

Find the average number of students studying in section B and C of 10th class.

Correct Answer: The correct option is 100 (Option 3).

Step-by-step Explanation:

Let us analyze the given information step-by-step to calculate the total number of students in each section.

1. Total Girls and Boys in 10th Class:

It is given that the total number of girls across all four sections (A, B, C, D) is 225.

The ratio of total boys to total girls is 8:9.

Therefore, total number of boys = $\frac{8}{9}\times 225=200$.

2. Information about Section C:

Number of girls in section C = 55.

The number of boys in section C is 10 less than the number of girls in section C.

Therefore, boys in section C = 55 - 10 = 45.

Total students in section C = 45 + 55 = 100.

3. Information about Section B and Section A:

Let the number of boys in section B be x.

Ratio of boys to girls in section B is 1:3, so girls in section B = 3x.

The number of girls in section A and section B is the same, so girls in section A = 3x.

4. Information about Section D:

The number of girls in section D is 5 less than the boys in section B.

So, girls in section D = x - 5.

5. Finding x (Boys in Section B):

Total girls = Girls in (A + B + C + D)

$3x+3x+55+(x-5)=225$

$7x+50=225$

$7x=175$

$x=25$

Thus:

Boys in section B = 25

Girls in section B = 3 × 25 = 75

Total students in section B = 25 + 75 = 100.

Girls in section A = 75

Girls in section D = 25 - 5 = 20

6. Calculating Average Students in Section B and C:

Total students in section B = 100

Total students in section C = 100

Average number of students in section B and C = $\frac{100+100}{2}=100$.