The average weight of some persons in a group is the 70 kg. When 15 persons with average weight 60 kg leave the group over 15 persons with average weight 87.5 kg join the group, then the average weight of persons in the group in both the cases is equal. How many persons were there in the group, initially?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 55.
Let the number of persons be N.
Initial total weights = 70N
According to the question,
⇒ (70N + 15 × 87.5)/(N + 15) = (70N - 15 × 60)/(N - 15)
⇒ (70N + 1312.5)(N - 15) = (70N - 900)(N + 15)
Solving the above equation;
⇒ N = (140N + 412.5)/(147.5)
⇒ 147.5N = 140N + 412.5
⇒ 7.5N = 412.5
⇒ N = 55