The average of 8persons increases by 1.5kg.if a person weighting 65kg is replaced by a new person. what could be the weight of the new person.
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Let : Weight of new person = x kg
Given :
- Total number of person = 8
- Person weighing 65kg is replaced by person weighing x kg
- Average increase by 1.5 kg
To find : Weight of new person (x)
Formula used :
Mean/average = sum of weight of all persons ÷ number of persons
Solution :
Let initial average = A
A = ( sum of weight of 7 persons + 65) ÷ 8
=> 8A = sum of weight of 7 persons + 65
=> Sum of weight of 7 persons = 8A - 65. ..... equation 1
Also
New average = Initial average + 1.5
New average = A + 1.5
Also ,
New average = ( Sum if age of 7 persons + x) ÷ 8
=> (A+1.5) = (Sum of age of 7 persons + x ) ÷ 8
putting value of "Sum of age of 7 persons " from equation 1 ,we get;
=> 8(A+1.5) = (8A-65) +x
=> 8A + 12 = 8A - 65 + x
=> x = 8A + 12 - 8A + 65
=> x = 77 kg
ANSWER : Weight of new person (x) = 77kg
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