In June `2018`, MEH had `9600` students. If the number of boys increases `8%` and no. of girls increases by `5%` then in july `2018` it had `10272` students. Then find no. of girls in july `2018` ?

Options

A. `3260`
B. `3265`
C. `3390`
D. `3360`

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the increase in the number of students
First, we need to find out how many students have increased from June 2018 to July 2018.

\[ \text{Increase in students} = \text{Total students in July} - \text{Total students in June} \]
\[ = 10272 - 9600 = 672 \]

### Step 2: Calculate the overall percentage increase
Next, we calculate the overall percentage increase in the number of students.

\[ \text{Percentage increase} = \left( \frac{\text{Increase}}{\text{Total in June}} \right) \times 100 \]
\[ = \left( \frac{672}{9600} \right) \times 100 \approx 7\% \]

### Step 3: Set up the percentage increase for boys and girls
We know from the problem that:
- The boys increase by 8%
- The girls increase by 5%
- The overall increase is 7%

### Step 4: Set up the allegation method
Using the allegation method, we can set up the differences:
- Difference between boys' increase and overall increase: \(8\% - 7\% = 1\%\)
- Difference between girls' increase and overall increase: \(7\% - 5\% = 2\%\)

### Step 5: Establish the ratio of boys to girls
The ratio of the increase in boys to girls can be established as follows:
\[ \text{Ratio} = \frac{2}{1} \quad \text{(boys : girls)} \]

### Step 6: Calculate the total parts in the ratio
The total parts in the ratio is:
\[ 2 + 1 = 3 \text{ parts} \]

### Step 7: Find the value of one part
Now, we can find the value of one part based on the total increase in students:
\[ \text{Total increase} = 672 \]
\[ \text{Value of one part} = \frac{672}{3} = 224 \]

### Step 8: Calculate the number of girls
Since the girls' increase corresponds to 1 part, we can find the number of girls who increased:
\[ \text{Increase in girls} = 1 \times 224 = 224 \]

### Step 9: Calculate the number of girls in July 2018
To find the total number of girls in July 2018, we need to find the initial number of girls in June 2018. Let \( g \) be the number of girls in June 2018. The number of boys in June 2018 would then be \( 9600 - g \).

Using the percentage increase for girls:
\[ g + 0.05g = g(1 + 0.05) = 1.05g \]
The total number of girls in July 2018 becomes:
\[ \text{Total girls in July} = 1.05g \]

### Step 10: Solve for girls in July
Since we know the increase in girls is 224, we can set up the equation:
\[ 1.05g - g = 224 \]
\[ 0.05g = 224 \]
\[ g = \frac{224}{0.05} = 4480 \]

Now, substituting back to find the number of girls in July:
\[ \text{Total girls in July} = 1.05 \times 4480 = 4704 \]

### Final Answer
The number of girls in July 2018 is **4704**.

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