In a co-educational school there are 15 more girls than boys. If the number of girls is increased by `10%` and the number of boys is also increased by `16%` there would be 9 more girls than boys. What is the number of students in the school?

Options

A. 140
B. 125
C. 265
D. 255

Answer

To solve the problem step by step, we will define variables, set up equations based on the information given, and then solve for the number of students in the school.

### Step 1: Define Variables
Let:
- \( x \) = number of boys in the school
- \( x + 15 \) = number of girls in the school (since there are 15 more girls than boys)

### Step 2: Set Up the Equations for Increases
According to the problem:
- The number of girls after a 10% increase is:
\[ (x + 15) \times 1.1 = 1.1(x + 15) \]
- The number of boys after a 16% increase is:
\[ x \times 1.16 = 1.16x \]

### Step 3: Set Up the Condition for the New Numbers
After the increases, it is stated that there are 9 more girls than boys:
\[ 1.1(x + 15) = 1.16x + 9 \]

### Step 4: Expand and Rearrange the Equation
Expanding the left side:
\[ 1.1x + 16.5 = 1.16x + 9 \]
Now, rearranging the equation to isolate \( x \):
\[ 1.1x + 16.5 - 9 = 1.16x \]
\[ 1.1x + 7.5 = 1.16x \]
Subtract \( 1.1x \) from both sides:
\[ 7.5 = 1.16x - 1.1x \]
\[ 7.5 = 0.06x \]

### Step 5: Solve for \( x \)
To find \( x \):
\[ x = \frac{7.5}{0.06} = 125 \]

### Step 6: Find the Number of Girls
Now that we have the number of boys, we can find the number of girls:
\[ \text{Number of girls} = x + 15 = 125 + 15 = 140 \]

### Step 7: Calculate the Total Number of Students
Finally, we can find the total number of students in the school:
\[ \text{Total students} = \text{Number of boys} + \text{Number of girls} = 125 + 140 = 265 \]

### Final Answer
The total number of students in the school is **265**.

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