Question : A group of boys has an average weight of 42 kg. One boy weighing 48 kg leaves the group and another boy weighing 38 kg joins the group. If the average now becomes 41 kg, then how many boys are there in the group?
Option 1: 8
Option 2: 10
Option 3: 12
Option 4: 6
Correct Answer: 10
Solution :
Given: A group of boys has an average weight of 42 kg.
We know the formula, Average = $\frac{\text{sum of weight of all the boys}}{\text{the number of boys}}$.
Let the boy's number be $x$.
⇒ $\frac{\text{sum of weight of all the boys}}{x}=42$
⇒ $42x=\text{sum of weight of all the boys}$ (equation 1)
One boy weighing 48 kg leaves the group and another boy weighing 38 kg joins the group.
⇒ $\frac{\text{sum of weight of all the boys–48+38}}{x}=41$
⇒ $41x=\text{sum of weight of all the boys}–10$
Substitute the value from the equation 1,
⇒ $41x=42x–10$
⇒ $42x–41x=10$
⇒ $x=10$
Hence, the correct answer is 10.
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