To solve this question, the user needs to know how to set up and solve a system of equations. Let the number of girls be x and the number of boys be y. We can then set up two equations based on the given information:
Equation 1: x + y = 45 (the total number of boys and girls is 45)
Equation 2: 0.50x + 1.00y = 39 (the total amount of money distributed is Rs 39)
Now, let's go through each option and see if it satisfies the equations:
A) If there are 10 girls, then there are 35 boys. This satisfies equation 1. The total amount of money given to girls is 0.50 * 10 = Rs 5. The total amount of money given to boys is 1.00 * 35 = Rs 35. The total amount of money distributed is Rs 5 + Rs 35 = Rs 40, which is not equal to Rs 39. Therefore, option A is incorrect.
B) If there are 12 girls, then there are 33 boys. This satisfies equation 1. The total amount of money given to girls is 0.50 * 12 = Rs 6. The total amount of money given to boys is 1.00 * 33 = Rs 33. The total amount of money distributed is Rs 6 + Rs 33 = Rs 39, which is equal to the given total amount. Therefore, option B is correct.
C) If there are 6 girls, then there are 39 boys. This satisfies equation 1. The total amount of money given to girls is 0.50 * 6 = Rs 3. The total amount of money given to boys is 1.00 * 39 = Rs 39. The total amount of money distributed is Rs 3 + Rs 39 = Rs 42, which is not equal to Rs 39. Therefore, option C is incorrect.
D) If there are 18 girls, then there are 27 boys. This satisfies equation 1. The total amount of money given to girls is 0.50 * 18 = Rs 9. The total amount of money given to boys is 1.00 * 27 = Rs 27. The total amount of money distributed is Rs 9 + Rs 27 = Rs 36, which is not equal to Rs 39. Therefore, option D is incorrect.
Thus, the correct answer is:
The Answer is: B) 12.