One third of the boys and one half of the girls in a college participate in a sports event. The total number of participating students is 300, out of which 100 are boys. What is the total number of students enrolled in the college?

Introduction / Context:
This is a percentage and ratio based counting problem involving boys and girls in a college. It tests your ability to convert fractions into actual numbers and to use the given participant information to determine total enrolment.

Given Data / Assumptions:

• One third of the boys participate in the sport.• One half of the girls participate in the sport.• Total participants in the event = 300 students.• Among these participants, 100 are boys.• We must find the total number of students in the college.

Concept / Approach:
Let the total number of boys be B and the total number of girls be G. The number of boys who participate is B/3, which is given as 100. The total participants are B/3 + G/2 = 300. From these two equations we can find B and G and then compute the total number of students B + G.

Step-by-Step Solution:
Step 1: From the given data, B/3 = 100.Step 2: So B = 100 * 3 = 300 boys in the college.Step 3: Total participants are B/3 + G/2 = 300.Step 4: Substitute B/3 = 100, we get 100 + G/2 = 300.Step 5: Therefore G/2 = 200 and G = 400.Step 6: Total students in the college = B + G = 300 + 400 = 700.

Verification / Alternative check:
Check participation counts. One third of 300 boys is 100, which matches the given number of participating boys. One half of 400 girls is 200. Total participants = 100 + 200 = 300, which exactly matches the question, confirming the calculation.

Why Other Options Are Wrong:
Values 550, 575 and 625 do not satisfy both the conditions simultaneously when you calculate the participating boys and girls according to the given fractions.

Common Pitfalls:
Many students wrongly assume that 100 boys represent one third of total students instead of one third of the boys only. Another mistake is to forget that the total 300 participants include both boys and girls.

Final Answer:
The total number of students in the college is 700.