9. in a group of 12 boys if two boys aged 14 and 18 are replaced by two other boys the average age drops by 1 year. what is the average age of the two new boys?
Answers
Answer:
10 years
Step-by-step explanation:
The average age of 12 boys decreased by 1 year, this means the total(sum) age of the boys decreased by (12x1) = 12 years.
==> So, the sum of ages of the two new boys = (14+18-12) = 20 years.
==>So. the average age of the two new boys = (20/2) = 10.
Given,
Total number of boys = 12
Age of two boys = 14 and 18
To Find,
The average age of two new boys due to which the average dropped by 1.
Solution,
The formula for calculating the average is
Average = sum of observation/number of observation
Let S' be the sum of age of the remaining 10 boys and the average be x
In first case
(12+14+S')/12 = x
Now, these two boys are relaced
(S'+b₁+b₂)/12 = x-1
(S'+b₁+b₂)/12+1 = x
Equating both the values of x
(12+14+S')+/12 = (S'+b₁+b₂)/12+12/12
26+S' = S'+b₁+b₂+12
b₁+b₂ = 14
(b₁+b₂)/2 = 14/2 = 7
Hence, the average age of the two new boys is 7.