Correct option is A
Given:
The ratio of girls to boys in Section 1 is 3:4.
The ratio of girls to boys in Section 2 is 3:7.
The overall girls to boys ratio in the entire class is 4:7.
We need to determine the possible number of girls in the entire class.
Concept Used:
Let the number of girls and boys in Section 1 be 3x and 4x respectively.
Let the number of girls and boys in Section 2 be 3y and 7y respectively.
The total number of girls in the class = 3x + 3y.
The total number of boys in the class = 4x + 7y.
Given that the total ratio of girls to boys is 4:7, we set up the equation:
(3x + 3y) / (4x + 7y) = 4/7
Cross multiplying:
7(3x + 3y) = 4(4x + 7y)
Expanding:
21x + 21y = 16x + 28y
Rearranging:
5x = 7y
So, x : y = 7 : 5.
Let x = 7k and y = 5k.
Then,
Total girls = 3x + 3y
= 3(7k) + 3(5k) = 21k + 15k = 36k
Solution:
The number of girls must be a multiple of 36.
Checking the options:
36 → Valid (36 = 36 × 1)
42 → (Not a multiple of 36)
45 → (Not a multiple of 36)
48 → (Not a multiple of 36)
Thus, the possible strength of girls in the entire class is 36.
Final Answer:
(A) 36
