average age of a group of people is four times the no of people in the group. Sakhi leaves the group and average age is still four times the no of people in the group. after that Sheetal leaves the group and average age is still four times the no of people. if ratio between Sakshi's age and Sheetal age is 21:19. then find the average age of the group if ritu leaves the group who age is 20 years
Answers
Answer:
38 Years
Step-by-step explanation:
Let say there are N people in Group
Average age of Group = 4N
Total Age of Group = N*4N = 4N²
Sakshi Leave the group => Numbe of People in group now = N-1
Average age of Group = 4(N-1)
Total Age of Group = 4(N-1)²
Sakshi Age = 4N² - 4(N-1)² = 4 (N + N -1)(1) = 4(2N - 1)
Sheetal Leave the group => Numbe of People in group now = N-2
Average age of Group = 4(N-2)
Total Age of Group = 4(N-2)²
Sheetal Age = 4(N-1)² - 4(N-2)² = 4 (N -1 + N -2)(1) = 4(2N - 3)
ratio between Sakshi's age and Sheetal age is 21:19.
4(2N - 1)/ 4(2N - 3) = 21/19
=> 19(2N-1) = 21(2N - 3)
=> 38N - 19 = 42N - 63
=> 4N = 44
=> N = 11
After leaving shakshi & Sheetal People in group = N -2 = 11 - 2 = 9
Average age = 4*9 = 36
Total Age = 9 * 36 = 324
Now ritu Leaves the group
number of people = 8
Age = 324 - 20 = 304
Average Age = 304/8 = 38 Years
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Verification
11 People Average Age = 44 Total age = 484
Shakshi Age = 84
10 People Average Age = 40 Total age = 400
Sheetal Age = 76
9 People Average Age = 36 Total age = 324
Ritu Age = 20
8 People Average Age = 38 Total age = 304