The ratio of the number oif boys to that of girls in a school is `9:11`. If the number of girls in the school is 2035, find:
a. number of boys is school.
b. number of students in school.

Answer

To solve the problem step by step, we will follow the given information about the ratio of boys to girls and the number of girls in the school.

### Step 1: Understand the Ratio
The ratio of boys to girls is given as \( 9:11 \). This means that for every 9 boys, there are 11 girls.

### Step 2: Set Up the Equation
Let the number of boys be represented as \( B \) and the number of girls as \( G \). According to the ratio, we can express this relationship as:
\[ \frac{B}{G} = \frac{9}{11} \]
We know that the number of girls \( G = 2035 \).

### Step 3: Substitute the Known Value
Substituting \( G \) into the ratio gives us:
\[ \frac{B}{2035} = \frac{9}{11} \]

### Step 4: Cross-Multiply to Solve for Boys
Cross-multiplying to solve for \( B \):
\[ B \cdot 11 = 9 \cdot 2035 \]
This simplifies to:
\[ B = \frac{9 \cdot 2035}{11} \]

### Step 5: Calculate the Number of Boys
Now we can calculate \( B \):
\[ B = \frac{9 \cdot 2035}{11} = \frac{18315}{11} = 1665 \]
So, the number of boys in the school is \( 1665 \).

### Step 6: Calculate the Total Number of Students
To find the total number of students in the school, we add the number of boys and girls:
\[ \text{Total Students} = B + G = 1665 + 2035 \]
Calculating this gives:
\[ \text{Total Students} = 3700 \]

### Final Answers
a. The number of boys in the school is \( 1665 \).
b. The total number of students in the school is \( 3700 \).

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