`40%` of the total number of students in a school are in primary classes. “`1/5th` of the remaining students are in secondary classes and the remaining 1200 are in higher secondary classes. What is the total number of students in the school ?

Options

A. 3500
B. 2250
C. 3000
D. 2500

Answer

To solve the problem, we will break it down step by step.

### Step 1: Define the total number of students
Let the total number of students in the school be denoted as \( T \).

### Step 2: Calculate the number of students in primary classes
According to the problem, 40% of the total students are in primary classes. Therefore, the number of students in primary classes is:
\[ \text{Students in Primary} = 0.4T \]

### Step 3: Calculate the remaining students after primary classes
The remaining students after accounting for those in primary classes can be calculated as:
\[ \text{Remaining Students} = T - 0.4T = 0.6T \]

### Step 4: Calculate the number of students in secondary classes
It is given that \( \frac{1}{5} \) of the remaining students are in secondary classes. Therefore, the number of students in secondary classes is:
\[ \text{Students in Secondary} = \frac{1}{5} \times 0.6T = 0.12T \]

### Step 5: Calculate the remaining students after secondary classes
Now, we need to find the remaining students after accounting for those in secondary classes:
\[ \text{Remaining Students after Secondary} = 0.6T - 0.12T = 0.48T \]

### Step 6: Set up the equation for higher secondary classes
According to the problem, the remaining students (which are in higher secondary classes) total 1200. Thus, we can set up the equation:
\[ 0.48T = 1200 \]

### Step 7: Solve for the total number of students
To find \( T \), we divide both sides of the equation by 0.48:
\[ T = \frac{1200}{0.48} = 2500 \]

### Conclusion
The total number of students in the school is \( \boxed{2500} \).

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