Question : The average weight of 8 students is 48 kg. If four students with an average weight of 44 kg and four with an average weight of 58 kg are also added, then find the average weight of 16 students.
Option 1: 49.5 kg
Option 2: 48 kg
Option 3: 49 kg
Option 4: 48.5 kg
Correct Answer: 49.5 kg
Solution :
The average weight of 8 students = 48 kg
Sum of the weights of 8 students = 48 × 8 = 384 kg
The average weight of 4 students = 44 kg
Sum of the weights of 4 students = 44 × 4 = 176 kg
The average weight of another 4 students = 58 kg
Sum of the weights of 4 students = 58 × 4 = 232 kg
Sum of the weights of 16 students = 384 + 176 + 232 = 792 kg
The average weight of 16 students = $\frac{\text{Sum of the weights of 16 students}}{\text{Total students}}=\frac{792}{16}= 49.5$
Hence, the correct answer is 49.5 kg.
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