In a class of 60 students, each boy contributes rupees equal to the number of girls and each girl contributes rupees equal to the number of boys. If the total contribution collected is Rs. 1600, how many girls are there in the class?

Introduction / Context:
This is a quantitative reasoning question involving two unknowns: the number of boys and the number of girls in a class. Each student contributes an amount of money equal to the number of students of the opposite gender. You are given the total number of students in the class and the total contribution collected. The task is to determine how many girls are in the class by forming and solving algebraic equations.

Given Data / Assumptions:
- Total number of students in the class is 60.
- Let the number of boys be B and the number of girls be G.
- Each boy contributes rupees equal to the number of girls, that is G rupees per boy.
- Each girl contributes rupees equal to the number of boys, that is B rupees per girl.
- Total contribution collected is Rs. 1600.
- The class is composed only of boys and girls, so B + G = 60.

Concept / Approach:
We translate the verbal description into two equations. One comes from the fact that the total number of students is 60. The other comes from equating the total rupee contribution to 1600. The total amount collected from boys is B * G, and from girls is G * B, for a total of 2 * B * G. This leads to a system of equations in B and G that can be solved using basic algebra and quadratic equations. Finally, we check which of the possible solutions matches the options given and makes sense for the number of girls.

Step-by-Step Solution:
Step 1: From the total number of students, we have B + G = 60. Step 2: Total contribution from boys is B * G (each boy pays G rupees), and total contribution from girls is G * B (each girl pays B rupees). Step 3: Therefore total contribution = B * G + G * B = 2 * B * G. Step 4: We are told that this total is Rs. 1600, so 2 * B * G = 1600, which gives B * G = 800. Step 5: Now we have a system of two equations: B + G = 60 and B * G = 800. Step 6: Express G in terms of B as G = 60 - B, and substitute into B * G = 800 to get B * (60 - B) = 800. Step 7: Expand this to obtain 60B - B^2 = 800, or B^2 - 60B + 800 = 0. Step 8: Solve the quadratic equation B^2 - 60B + 800 = 0. The discriminant is 60^2 - 4 * 1 * 800 = 3600 - 3200 = 400. Step 9: The square root of 400 is 20, so B = (60 ± 20) / 2, giving B = 40 or B = 20. Step 10: For B = 40, G = 60 - 40 = 20. For B = 20, G = 60 - 20 = 40.

Verification / Alternative check:
Check both possible pairs. If there are 40 boys and 20 girls, then each boy contributes 20 rupees and each girl contributes 40 rupees. Total contribution is 40 * 20 + 20 * 40 = 800 + 800 = 1600. If there are 20 boys and 40 girls, each boy contributes 40 rupees and each girl contributes 20 rupees, giving the same total 20 * 40 + 40 * 20 = 1600. Thus both (B, G) = (40, 20) and (20, 40) satisfy the conditions, but the question specifically asks for the number of girls and provides answer options among which only 40 appears. Hence the number of girls is 40, which corresponds to the valid solution B = 20, G = 40.

Why Other Options Are Wrong:
- Option 30 does not satisfy B + G = 60 when combined with any integer B that also gives B * G = 800.
- Option 25 likewise fails to satisfy both the sum and the product conditions simultaneously.
- Option 15 cannot pair with any B such that both the sum is 60 and the total contribution equals 1600.

Common Pitfalls:
A common mistake is to forget that boys and girls play symmetric roles in the equations, which leads to two possible solutions. Some students pick the first solution they find without checking the other, or they mistakenly believe only one solution can exist. Others may set up the product equation incorrectly, missing the factor of 2. Careful algebra and a quick verification of all solutions against the answer options help avoid these errors.

Final Answer:
The configuration that fits both the total number of students and the total contribution and matches one of the given options is the one with 40 girls in the class.