Question : A group of students has an average weight of 42 kg. One student of weight 48 kg leaves the group and another student of weight 44 kg joins the group. If the new average weight becomes 41.6 kg, then how many students are there in the group?
Option 1: 15
Option 2: 10
Option 3: 8
Option 4: 12
Correct Answer: 10
Solution :
Let's denote the number of students in the original group as N
So, Total weight = 42N
When one student weight 48 kg leaves and another student weight 44 kg joins
⇒ Total weight = 42N – 48 + 44
Since the new average weight is given as 41.6 kg
⇒ $\frac{42N-48+44}{N}$ = 41.6
⇒ ${42N-48+44} = 41.6N$
⇒ 42N − 41.6N = 48 − 44
⇒ 0.4N = 4
⇒ N = 10
Hence, the correct answer is 10.
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