Question

The average weight of 16 boys in a class is 50.25 kgs and that of the remaining 8 boys is 45.15 kgs. Find the average weight of all the boys in the class?

• A. 48.55 kgs
• B. 48 kgs
• C. 47.55 kgs
• D. 49.25 kgs
• E. 50.25 kgs

Hint:

Average of combined groups = (sum of all values) / (total number of items).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Calculate the weighted average of two groups.
Step 2: Key Formula or Approach:
Combined Average = \( \frac{n_1 a_1 + n_2 a_2}{n_1 + n_2} \).
Step 3: Detailed Explanation:
1. Total weight of 16 boys = \( 16 \times 50.25 = 804 \) kgs.
2. Total weight of 8 boys = \( 8 \times 45.15 = 361.2 \) kgs.
3. Total students = \( 16 + 8 = 24 \).
4. Combined average = \( \frac{804 + 361.2}{24} = \frac{1165.2}{24} \).
5. Calculation: \( 1165.2 \div 24 = 48.55 \).
Step 4: Final Answer:
The overall average weight is 48.55 kgs.