Question : The average weight of 12 persons increases by 3.5 kg when a new person comes in place of one of them weighing 58 kg. The weight of the new person is:
Option 1: 100 kg
Option 2: 16 kg
Option 3: 70 kg
Option 4: 42 kg
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Correct Answer: 100 kg
Solution :
Let the average weight of 12 persons be $x$.
Total weight of 12 persons = $12x$
If a person with 58 kg weight is replaced by a new person of $y$ kg weight,
Average weight increases by 3.5 kg.
⇒ $12x - 58 + y = 12(x + 3.5)$
⇒ $12x - 58 + y = 12x + 42$
$\therefore y = 58 + 42 = 100$ kg
Hence, the correct answer is 100 kg.
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