Question : A group of boys has an average weight of 36 kg. One boy weighing 42 kg leaves the group and another boy weighing 30 kg joins the group. If the average now becomes 35.7 kg, then how many boys are there in the group?
Option 1: 30
Option 2: 32
Option 3: 40
Option 4: 56
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Correct Answer: 40
Solution :
Let the number of boys be $x$.
The total weight of the boys is $36x$ kg.
Now one boy weighing 42 kg leaves the group and another boy weighing 30 kg joins the group,
⇒ Total weight of the boys = $(36x - 42 + 30) = (36x – 12)$ kg
According to the question,
$(\frac{36x-12}{x}) = 35.7$
⇒ $36x-35.7x = 12$
$\therefore x = \frac{12}{0.3} = 40$
Hence, the correct answer is 40.
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