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?

Step-by-Step Solution1. Analyze the Boy's Data:We are told that 100 boys participated in the project.The problem states that these 100 boys represent one-third ($\frac{1}{3}$) of the total number of boys in the college.Let $B$ be the total number of boys:$$\frac{1}{3}B = 100$$$$B = 100 \times 3 = \mathbf{300 \text{ boys}}$$2. Analyze the Girl's Data:There were 300 total participants, and 100 of them were boys.Therefore, the number of girls who participated is:$$300 - 100 = \mathbf{200 \text{ girls participating}}$$The problem states that these 200 girls represent one-half ($\frac{1}{2}$) of the total number of girls in the college.Let $G$ be the total number of girls:$$\frac{1}{2}G = 200$$$$G = 200 \times 2 = \mathbf{400 \text{ girls}}$$3. Calculate the Total Students:Total Students = Total Boys + Total Girls$$300 + 400 = \mathbf{700}$$