One-third of the boys and one-half of the girls of a college participated in a social work project. If the number of participating students is 300 out of which 100 are boys, what is the total number of students in the college?

### Concept & Logic This problem can be resolved using simple algebraic formulation or backwards arithmetic. By identifying the exact number of participating boys and girls, we can determine the total number of boys and girls in the college independently. ### Step-by-Step Solution * **Given:** * Total participating students = $300$ * Participating boys = $100$ * Therefore, participating girls = $300 - 100 = 200$ * **Calculation:** * Let the total number of boys in the college be $B$ and girls be $G$. * According to the problem: $$ \frac{1}{3} \times B = 100 \implies B = 300 $$ $$ \frac{1}{2} \times G = 200 \implies G = 400 $$ * Total number of students = $B + G = 300 + 400 = 800$ ### Exam Strategy & Shortcut Directly scale up the parts: * If $\frac{1}{3}$ of boys is 100, then total boys must be $100 \times 3 = 300$. * If $\frac{1}{2}$ of girls is $(300 - 100) = 200$, then total girls must be $200 \times 2 = 400$. * Quickly sum them up mentally: $300 + 400 = 800$. ### Common Pitfall Misreading the question and assuming that 100 boys represents the total number of boys in the college instead of the *participating* boys. Read carefully to distinguish between the total population and the sub-group components. ### Final Answer **Therefore, the correct answer is 800.**