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A group of people consists of men, women, and children. 40% of them are men, 35% are women and rest are children, and their average weights are 70 kg, 60 kg and 30 kg, respectively. The average weight of the group is:
45.5 kg
46.5 kg
55.5 kg
56.5 kg
55.5 kg
Assume total 100 people: 40 men, 35 women, 25 children. Multiply each group's count by their average weight, sum them up, and divide by 100.
Men = 40%, Women = 35%, Children = 25%. Average weight of men = 70 kg, women = 60 kg, children = 30 kg.
Average Weight=Total NumberTotal Weight=100w1p1+w2p2+w3p3
Assume total 100 people: 40 men, 35 women, 25 children. Multiply each group's count by their average weight, sum them up, and divide by 100.
Forgetting to calculate the percentage of children as 100−(40+35)=25%.
Step 1: Determine the percentage of children
Since total percentage must be 100%, the percentage of children is given by 100−(40+35).
Children=100%−75%=25%
Step 2: Calculate the total weight for 100 people
Multiply the percentage (number of people out of 100) of each category by their respective average weight and sum them up.
Wtotal=(40×70)+(35×60)+(25×30)
Step 3: Evaluate products
Compute the total weight for men, women, and children.
Wtotal=2800+2100+750=5650 kg
Step 4: Calculate the average weight of the group
Divide the total weight by the total number of people (100).
Average=1005650=56.5 kg
D is correct because the calculated average weight of the group is 56.5 kg.
Weighted average problems frequently appear in mixtures, alligations, and statistics questions across competitive exams.
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