The total number of students in a school is 2140. If the number of girls in the school is 1200, then what is the ratio of the total number of boys to the total number of girls in the school ?

Options

A. ` 26 : 25 `
B. `47 : 60`
C. `18 : 13`
D. `31 : 79`

Answer

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

### Step 1: Determine the total number of boys
We know the total number of students in the school and the number of girls. The total number of boys can be calculated by subtracting the number of girls from the total number of students.

\[ \text{Total number of boys} = \text{Total number of students} - \text{Number of girls} \]

Substituting the values:

\[ \text{Total number of boys} = 2140 - 1200 = 940 \]

### Step 2: Write the ratio of boys to girls
Now that we have the total number of boys (940) and the total number of girls (1200), we can express the ratio of boys to girls.

\[ \text{Ratio of boys to girls} = \frac{\text{Total number of boys}}{\text{Total number of girls}} = \frac{940}{1200} \]

### Step 3: Simplify the ratio
To simplify the ratio, we can divide both the numerator and the denominator by their greatest common divisor (GCD).

First, we can simplify the fraction:

\[ \frac{940 \div 20}{1200 \div 20} = \frac{47}{60} \]

### Step 4: State the final ratio
Thus, the ratio of the total number of boys to the total number of girls in the school is:

\[ \text{Ratio of boys to girls} = 47 : 60 \]

### Summary of the Solution
The ratio of the total number of boys to the total number of girls in the school is 47:60.

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