Question
The average weight of 8 people is 75 kg. When three new
people with their weights in the ratio 3:4:5 joined the group, the average weight of all the people remains the same. Find the difference between the weights of the lightest and the heaviest new people who joined the group.Solution
ATQ, Sum of the weight of 8 people = 75 × 8 = 600 kg Sum of the weights of all the people including the ones who joined later = 75 × 11 = 825 kg Total weight of three new people = 825 - 600 = 225 kg Let the weights of the three new people who joined the group be '3y', '4y', and '5y' kg, respectively. 3y + 4y + 5y = 225 Or, 'y' = (225/12) = 18.75 So, required difference between the heaviest and the lightest = 5y - 3y = 2y = 2 × 18.75 = 37.5 kg
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