One-third of the boys and one-half of the girls in a college participate in a sports event. If 300 students participate in total and 100 of them are boys, what is the total number of students in the college?

Introduction / Context:
This aptitude question tests understanding of percentages, fractions, and basic algebra involving two groups, boys and girls, in a college. The goal is to convert the verbal conditions into equations and then determine the total strength of the college based on how many students participate in a sports event. This pattern of question is very common in competitive exams because it checks comfort with percentages and translation of words into numbers.

Given Data / Assumptions:

• One-third of the boys participate in the event.
• One-half of the girls participate in the event.
• Total participating students are 300.
• Out of these 300 participants, 100 are boys.
• Total number of students equals total boys plus total girls.

Concept / Approach:
The idea is to represent the number of boys and girls using variables, and then use the percentage information to build equations. Since we know exactly how many participating boys there are, that gives us one direct equation. The total number of participants gives a second equation. Solving these gives the total number of boys and girls separately, and adding them gives the total student population. This is a straightforward system of linear equations in two variables.

Step-by-Step Solution:
Step 1: Let the total number of boys be B and the total number of girls be G.Step 2: One-third of the boys participate, and the number of participating boys is given as 100. So (1/3) * B = 100, which implies B = 300.Step 3: Total participants are 300. Out of them, 100 are boys, so participating girls are 300 - 100 = 200.Step 4: One-half of the girls participate, so (1/2) * G = 200, which implies G = 400.Step 5: The total number of students in the college is B + G = 300 + 400 = 700.

Verification / Alternative check:
Check the fractions with the found values. One-third of 300 boys is 100, which matches the given participating boys. One-half of 400 girls is 200, which together with 100 boys gives 300 total participants. All given conditions are satisfied, so the answer is consistent and verified.

Why Other Options Are Wrong:
For 500, there is no way to split into boys and girls while keeping the given participation numbers of 100 boys and 200 girls. For 300, that would mean everyone is participating, contradicting the fraction conditions. For 600, the participation fractions would not match the given participant counts. For 650, similar algebra would fail to produce one-third equal to 100 and one-half equal to 200. Only 700 allows both equations to hold simultaneously.

Common Pitfalls:
Many students confuse the total number of participants with the total number of students or treat the given percentages as percentages of 300 rather than as fractions of the separate boy and girl populations. Another common mistake is to misread that 100 are boys and assume 200 are girls without then using the one-half relationship correctly. Careful reading and systematic use of variables help to avoid these mistakes.

Final Answer:
The total number of students in the college is 700, so the correct option is 700.