The ratio of 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`?

Options

A. 90
B. 120
C. 220
D. 240

Answer

To solve the problem step by step, we need to determine how many more girls should be admitted to make the ratio of boys to girls equal to 1:1.

### Step 1: Understand the Given Ratio
The ratio of boys to girls is given as 7:5. This means for every 7 boys, there are 5 girls.

### Step 2: Calculate Total Parts in the Ratio
Add the parts of the ratio together:
- Boys = 7 parts
- Girls = 5 parts
- Total parts = 7 + 5 = 12 parts

### Step 3: Determine the Value of Each Part
We know the total number of students in the school is 720. To find the value of one part, we divide the total number of students by the total parts:
\[ \text{Value of one part} = \frac{720}{12} = 60 \]

### Step 4: Calculate the Number of Boys and Girls
Now, we can calculate the number of boys and girls:
- Number of boys = 7 parts × 60 = 420
- Number of girls = 5 parts × 60 = 300

### Step 5: Set Up the Equation for 1:1 Ratio
To make the ratio of boys to girls equal to 1:1, the number of boys must equal the number of girls. Since we have 420 boys, we need to have 420 girls as well.

### Step 6: Calculate the Number of Additional Girls Needed
Currently, there are 300 girls. To find out how many more girls need to be admitted:
\[ \text{Additional girls needed} = 420 - 300 = 120 \]

### Conclusion
Therefore, **120 more girls should be admitted** to make the ratio of boys to girls equal to 1:1.

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