Question
In a company team, if 3 employees each weighing 65 kg
resign, the average weight of the remaining team members drops by 1 kg. But if 4 employees with an average weight of 66 kg resign, the average weight reduces by 2 kg. What was the original number of employees in the team?Solution
ATQ,
Let the total number of employees = n, and average weight = m
After 3 people leave:
mn - 3×65 = (n - 3)(m - 1)
→ mn - 195 = mn - 3m - n + 3
→ 3m + n = 198 -------- (i)
After 4 people leave:
mn - 4×66 = (n - 4)(m - 2)
→ mn - 264 = mn - 4m - 2n + 8
→ 4m + 2n = 272
→ divide by 2: 2m + n = 136 -------- (ii)
Now solve equations:
From (i): n = 198 - 3m
Substitute into (ii):
2m + (198 - 3m) = 136
→ 2m + 198 - 3m = 136
→ -m = -62
→ m = 62
→ n = 198 - 3×62 = 198 - 186 = 12
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