Question

In a class of 24 students, if one new student weighing 72 kg is added, then average weight of the class is increased by 1 kg. If one more student weighing 61 kg is added, then the average weight of the class increases by 1.5 kg over the initial average. What is the initial average weight (in kg) of the class?

• A. 50 kgs
• B. 47 kgs
• C. 57 kgs
• D. 50 kgs

Answer 1

The Correct Option is B

Finding the Initial Average Weight 

Step 1: Define Variables

Let the initial average weight be \( x \) kg.

The total weight of 24 students is:

\[ 24x \]

Step 2: Account for the New Student

After adding a 72 kg student, the new average weight becomes \( x + 1 \).

The new total weight equation is:

\[ \frac{24x + 72}{25} = x + 1 \]

Step 3: Solve for \( x \)

Multiply both sides by 25 to eliminate the fraction:

\[ 24x + 72 = 25x + 25 \]

Rearrange the equation:

\[ 24x - 25x = 25 - 72 \]

\[ -x = -47 \]

\[ x = 47 \]

Final Answer:

Thus, the initial average weight is 47 kg (Option B).