Question
In a group, 2 people with average weight 55 kg leave,
and the average drops by 1 kg. If 3 people of average weight 56 kg leave, average drops by 2 kg. Find original number of people.Solution
ATQ,
mn - 110 = (n - 2)(m - 1)
→ mn - 110 = mn - n - 2m + 2
→ n + 2m = 112 -------- (i)
mn - 168 = (n - 3)(m - 2)
→ mn - 168 = mn - 2n - 3m + 6
→ 2n + 3m = 174 -------- (ii)
Multiply (i) by 2: 2n + 4m = 224
Subtract (ii):
2n + 4m - 2n - 3m = 224 - 174
→ m = 50
→ n = 112 - 2×50 = 12
Hence, answer is 12 people
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