A student on his birthday distributed on an average 5 chocolates per student. If on the arrival of the teacher and the headmaster to whom the student gives 10 and 15 chocolates respectively, the average chocolate distributed per head increases to 5.5. How many students were in the class?

Answer

To solve the problem step by step, let's denote the number of students in the class as \( N \).

### Step 1: Calculate the total chocolates distributed initially
The student distributed chocolates at an average of 5 chocolates per student. Therefore, the total number of chocolates distributed to the students can be calculated as:
\[ \text{Total chocolates to students} = 5 \times N \]

### Step 2: Calculate the total chocolates after the teacher and headmaster arrive
When the teacher arrives, the student gives 10 chocolates, and when the headmaster arrives, he gives 15 chocolates. Therefore, the total chocolates distributed becomes:
\[ \text{Total chocolates} = 5N + 10 + 15 = 5N + 25 \]

### Step 3: Calculate the new average after the teacher and headmaster arrive
The total number of individuals now is \( N + 2 \) (the students plus the teacher and headmaster). The new average chocolates distributed per head is given as 5.5. Therefore, we can set up the equation:
\[ \frac{5N + 25}{N + 2} = 5.5 \]

### Step 4: Solve the equation
To eliminate the fraction, we can multiply both sides by \( N + 2 \):
\[ 5N + 25 = 5.5(N + 2) \]
Expanding the right side:
\[ 5N + 25 = 5.5N + 11 \]

Now, rearranging the equation to isolate \( N \):
\[ 25 - 11 = 5.5N - 5N \]
\[ 14 = 0.5N \]
Dividing both sides by 0.5:
\[ N = \frac{14}{0.5} = 28 \]

### Conclusion
The number of students in the class is \( N = 28 \).

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