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The average weight of 8 men increases by 1.5kg when one man weighing 65kg is replaced by a new man.
What is the weight of the new man?
75 kg
76 kg
77 kg
78 kg
77 kg
Multiply the number of people by the increase in average and add it to the weight of the replaced person: 8├Ч1.5+65=12+65=77 kg.
Number of men = 8, increase in average weight = 1.5 kg, weight of the replaced man = 65 kg.
New┬аWeight=Weight┬аof┬аreplaced┬аman+(Number┬аof┬аmen├ЧIncrease┬аin┬аaverage)
Multiply the number of people by the increase in average and add it to the weight of the replaced person: 8├Ч1.5+65=12+65=77 kg.
Many students multiply the increase by the weight of the replaced man or subtract the increment instead of adding it when the average increases.
Calculate the total weight increase
Since the average weight increases by 1.5 kg for all 8 men, the total weight of the group increases by 8 times 1.5 kg.
8├Ч1.5=12┬аkg
Determine the new man's weight
The new man's weight must be the weight of the replaced man plus the total increase in weight of the group.
Weight=65+12=77┬аkg
C is correct because the new man's weight is calculated as 65+(8├Ч1.5)=77 kg.
This concept is a subset of 'replacement problems' frequently found in Allegations and Mixtures or simple interest problems where a change in a single entity affects the total group average.
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