The total number of students in a school is 8670. If the number of boys in the school is 4545, then what will be the ratio of the number of boys to the total number of girls in the school ?

Options

A. `303 : 275`
B. `275 : 303`
C. `11 : 12`
D. `12 : 11`

Answer

To find the ratio of the number of boys to the total number of girls in the school, we can follow these steps:

### Step 1: Determine the total number of students
The total number of students in the school is given as 8670.

### Step 2: Determine the number of boys
The number of boys in the school is given as 4545.

### Step 3: Calculate the number of girls
To find the number of girls, we subtract the number of boys from the total number of students:

\[ \text{Number of girls} = \text{Total students} - \text{Number of boys} \]
\[ \text{Number of girls} = 8670 - 4545 \]
\[ \text{Number of girls} = 4125 \]

### Step 4: Set up the ratio of boys to girls
Now, we need to find the ratio of the number of boys to the number of girls:

\[ \text{Ratio of boys to girls} = \frac{\text{Number of boys}}{\text{Number of girls}} = \frac{4545}{4125} \]

### Step 5: Simplify the ratio
To simplify the ratio, we can divide both the numerator and the denominator by their greatest common divisor (GCD).

Calculating the GCD of 4545 and 4125:
- The GCD of 4545 and 4125 is 225.

Now we can simplify the ratio:

\[ \frac{4545 \div 225}{4125 \div 225} = \frac{20.2}{18.33} \approx \frac{20}{18} \text{ (after rounding)} \]

To get the final simplified ratio, we can express it in whole numbers:

\[ \text{Ratio} = \frac{4545}{4125} = \frac{91}{82} \]

Thus, the ratio of the number of boys to the total number of girls in the school is:

\[ \text{Ratio of boys to girls} = 91:82 \]