The ratio of the number of boys and girls in a school of 720 students is 7 : 5. How many more girls should be admitted to make the ratio 1 : 1? (P.C.S., 2009)

### Concept & Equating Ratios To make a ratio $1 : 1$, the absolute quantities of both categories must become equal. First, find the initial quantities of boys and girls using the given ratio and total sum. ### Step-by-Step Solution * **Given:** Total number of students = $720$. Initial ratio of Boys to Girls = $7 : 5$. * Total parts in the ratio = $7 + 5 = 12$. * Value of one part = $\frac{720}{12} = 60$. * Number of boys = $7 \times 60 = 420$. * Number of girls = $5 \times 60 = 300$. * We want the new ratio to be $1 : 1$, which means the number of girls must equal the number of boys. * Required number of girls = $420$. * Number of *more* girls to be admitted = Target Girls - Current Girls * More girls needed = $420 - 300 = 120$. ### Exam Strategy & Shortcut Notice the gap in the ratio components. The ratio is $7 : 5$, meaning boys are $2$ parts ahead of girls. To make the ratio $1:1$ ($7:7$), girls need to gain exactly $2$ parts. Since $12 \text{ parts} = 720$, $1 \text{ part} = 60$. The required $2 \text{ parts} = 2 \times 60 = 120$. This allows you to solve the question mentally in seconds. ### Common Pitfall Calculating the number of girls and mistakenly selecting $300$ as the answer, forgetting that the question specifically asks for "how many *more* girls should be admitted". ### Final Answer Therefore, the correct answer is **120**.