The average weight of a group of boys is 40 kg. after a boy of weight 48 kg joins the group, the average weight of the group goes up by 1 kg. find the number of boys in the group originally.
Answers
x/y=40
x=40y
(x+48)/(y+1)=41
40y+48=41(y+1)
40y+48=41y+41
48-41=41y-40y
y=7
There were 7 boys originally
Number of boys in group is 7
Given:
The average weight of a group of boys is 40 kg
After joining a boy of weight 48 kg joins the group, the average weight of the group goes up by 1 kg
To find:
Find the number of boys in the group originally
Solution:
Let x be the number boys in group
The average of x number of boy ages = Sum of ages / x
From given data,
Sum of ages / x = 40 kg
⇒ Sum of ages = 40x
After joining a boy of weight 48 kg in the group, the average weight of the group goes up by 1 kg i.e 41 kg and number of boys will be (x+1)
The average of x+1 number of boy ages = Sum of ages of (x+1) boys / x+1
Sum of ages of (x+1) boys / x+1 = 41
Sum of ages of (x+1) boys = 41(x+1)
As we know sum of age of x number of boys = 40x
After joining a boy of weight 48 kg, Sum of age = 40x+48
⇒ Sum of ages of (x+1) boys = 40x + 48
⇒ 40x+48 = 41(x+1)
⇒ 40x + 48 = 41x + 41
⇒ 41x - 40x = 48 - 41
⇒ x = 7
Therefore, Number of boys in group = 7
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