A group has certain number of people. If 2 people of average weight 64 kg left the group then the average weight of remaining people decreases by 1 kg. If 3 people of average weight 66 kg left the group then average weight of remaining people decreases by 2 kg. Find the number of people in the group.

Let the number of people in group and average weight of group be 'n' and 'm' kg, respectively. So, mn - 2 X 64 = (n - 2) X (m - 1) Or, mn - 128 = mn - n - 2m + 2 Or, 2m + n = 130 --------- (I) And, mn - 3 X 66 = (n - 3) X (m - 2) Or, mn - 198 = mn - 2n - 3m + 6 Or, 2n + 3m = 204 --------(II) On solving 2 X equation I - equation II, We get, 2 X (2m + n) - (2n + 3m) = 2 X 130 - 204 Or, 4m + 2n - 2n - 3m = 260 - 204 Or, 'm' = 56 Put m = 56 in equation I, 2(56) + n = 130 Or, 112 + n = 130 Or, 'n' = 18