The average weight of a class of students is 67.5kg. The weight of the class teacher is `25%` more than the average weight of the class. The average weight of the class is less than the class teacher by x%` .The value of x is :

Options

A. `33.33%`
B. `25%`
C. `20%`
D. can't be determined

Answer

To solve the problem step by step, we need to find the value of \( x \) which represents the percentage by which the average weight of the class is less than the weight of the class teacher.

### Step 1: Find the weight of the class teacher
The average weight of the class is given as \( 67.5 \) kg. The weight of the class teacher is \( 25\% \) more than the average weight of the class.

To calculate this, we first find \( 25\% \) of \( 67.5 \) kg:
\[ 25\% \text{ of } 67.5 = \frac{25}{100} \times 67.5 = 16.875 \text{ kg} \]

Now, we add this amount to the average weight of the class to find the weight of the class teacher:
\[ \text{Weight of class teacher} = 67.5 + 16.875 = 84.375 \text{ kg} \]

### Step 2: Calculate the difference in weight
Next, we need to find the difference between the weight of the class teacher and the average weight of the class:
\[ \text{Difference} = \text{Weight of class teacher} - \text{Average weight of class} = 84.375 - 67.5 = 16.875 \text{ kg} \]

### Step 3: Calculate the percentage difference
Now, we will find out by what percentage the average weight of the class is less than the weight of the class teacher. We use the formula for percentage:
\[ x\% = \left( \frac{\text{Difference}}{\text{Weight of class teacher}} \right) \times 100 \]
Substituting the values we have:
\[ x\% = \left( \frac{16.875}{84.375} \right) \times 100 \]

### Step 4: Simplify the calculation
Calculating the fraction:
\[ \frac{16.875}{84.375} = 0.2 \]
Now, multiply by \( 100 \):
\[ x\% = 0.2 \times 100 = 20\% \]

### Conclusion
Thus, the value of \( x \) is \( 20\% \).