Question : In a hotel, there are 120 staff members. Their average weight is 62.5 kg. When one of the staff members leaves the hotel, the average weight is reduced by 250 g. Find the weight of the staff member who left the hotel.
Option 1: 64.25 kg
Option 2: 78.75 kg
Option 3: 90.50 kg
Option 4: 92.25 kg
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Correct Answer: 92.25 kg
Solution :
Total number of staff members initially = 120
Their average weight = 62.5 kg
We know, Average = $\frac{\text{Sum of weights}}{\text{Number of people}}$
So, $62.5 = \frac{\text{Sum of weights}}{120}$
or, Sum of weights = 7500 kg
After a staff member left, the number of staff members = 119
Their average weight = 62.25 kg
Again, Average = $\frac{\text{Sum of weights}}{\text{Number of people}}$
So, $62.25 = \frac{\text{Sum of weights}}{119}$
or, Sum of weights = 7407.75 kg
So, the weight of the person who left = Old sum of weights – new sum of weights
= 7500 – 7407.75
= 92.25 kg
Hence, the correct answer is 92.25 kg.
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