Question
A group contains some number of members. If 2 members
with an average weight of 61 kg leave the group, the average weight of the remaining members decreases by 1 kg. If 3 members with an average weight of 62 kg leave the group, the average weight of the remaining members decreases by 2 kg. Find the number of members initially in the group.Solution
ATQ,
Let the number of members in group and average weight of group be 'n' and 'm' kg, respectively.
So,
mn - 2 × 61 = (n - 2) × (m - 1)
Or, mn - 122 = mn - n - 2m + 2
Or, 2m + n = 124 --------- (I)
And,
mn - 3 × 62 = (n - 3) × (m - 2)
Or, mn - 186 = mn - 2n - 3m + 6
Or, 2n + 3m = 192 -------- (II)
On solving 3 × equation (I) - 2 × equation (II),
We get, 3 × (2m + n) - 2 × (2n + 3m) = 3 × 124 - 2 × 192
Or, 6m + 3n - 4n - 6m = 372 - 384
Or, -n = -12
Thus, 'n' = 12
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