Question
A group consists of a certain number of individuals. If two
members, each weighing 59 kg, leave the group, the average weight of the remaining members decreases by 1 kg. Alternatively, if three members, each weighing 60 kg, leave the group, the average weight of the remaining members decreases by 2 kg. Determine the total number of individuals initially present in the group.Solution
Let the number of people in group and average weight of group be 'n' and 'm' kg, respectively.
So, mn - 2 X 59 = (n - 2) X (m - 1)
Or, mn - 118 = mn - n - 2m + 2
Or, 2m + n = 120 --------- (I)
And, mn - 3 X 60 = (n - 3) X (m - 2)
Or, mn - 180 = mn - 2n - 3m + 6
Or, 2n + 3m = 186 --------(II)
On solving 3 X equation I - 2 X equation II,
We get, 3 X (2m + n) - 2 X (2n + 3m) = 3 X 120 - 2 X 186
Or, 6m + 3n - 4n - 6m = 360 - 372
Or, 'n' = 12
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