A group has certain number of people. If 2 people of average weight 59 kg left the group then the average weight of remaining people decreases by 1 kg. If 3 people of average weight 61 kg left the group then average weight of remaining people decreases by 2 kg. Find the number of people 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 61 = (n - 3) X (m - 2)

Or, mn - 183 = mn - 2n - 3m + 6

Or, 2n + 3m = 189 --------(II)

On solving 2 X equation I - equation II,

We get, 2 X (2m + n) - (2n + 3m) = 2 X 120 - 189

Or, 4m + 2n - 2n - 3m = 240 - 189

Or, 'm' = 51

On putting value of 'm' in equation I,

We get, 2 X 51 + n = 120

Or, n = 18