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The average age of 40 boys in a class is 18 years. One boy, aged 26 years left the class, and two new boys joined the class. If the average age of all boys now in the class remains 18 years, then find the average age of the two newcomers.
21 years
20 years
22 years
24 years
22 years
Since the average remains unchanged at 18, the excess age brought by the two newcomers over the average must exactly compensate for the age of the boy who left. Thus, Sum of new boys = 18 + 18 + (26 - 18) = 44. Average of 2 newcomers = 44 / 2 = 22.
Initial number of boys = 40, Initial average age = 18 years. Age of boy who left = 26 years. Number of boys who joined = 2. Final average age = 18 years.
Average=NumberofitemsTotal┬аSumтАЛ
Since the average remains unchanged at 18, the excess age brought by the two newcomers over the average must exactly compensate for the age of the boy who left. Thus, Sum of new boys = 18 + 18 + (26 - 18) = 44. Average of 2 newcomers = 44 / 2 = 22.
Many students calculate the new total sum incorrectly by forgetting that the count of boys becomes 41 (40 - 1 + 2) and they must equate the sum to 41├Ч18.
Calculate initial sum
The initial total age of 40 boys with an average of 18 is 40├Ч18=720.
720
Adjust sum after 1 boy leaves
After a 26-year-old boy leaves, the new total is 720тИТ26=694.
694
Calculate final total age
There are now 40тИТ1+2=41 boys. The average is still 18, so the final total is 41├Ч18=738.
738
Find average of newcomers
The sum of the two newcomers is 738тИТ694=44. The average is 44/2=22.
22
C is correct because the sum of the ages of the two newcomers is 44, making their average 22 years.
This concept of 'replacement' in averages is identical to problems involving total weight change or income shifts in Data Interpretation sections.
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