When a student Joe, weighing 41 kg, joins a group of students whose av

Just a series of calculations, nothing more than that. When you see problems like this, start by trying to figure out whatever new tidbits of data you can deduce using the information in the passage. Then use that new data to deduce even more data that will eventually lead to the answer.

Knowing Joe's weight and the exact influence his weight has on the average weight of the group, we should be able to figure out the number of people (n) that were originally in that group, using the formula to calculate the average of any set of numbers.

\((30n + 41)/(n + 1) = 31\)

Doing some simple math there gives us n = 10. With Joe having thrown his weight into the group, we now have 11 people in this group, with the total weight now being 341 kgs (which we deduced from \(30n + 41\)) . Now we know that when 2 certain people in that group leave, the average weight returns back to 30. We could figure out the collective weight (w) of those two people in the group then, once again using the average formula.

\((341 - w)/9 = 30\)

Doing some more remedial math gives us w = 71, which means the average weight of the two people that left the group is 35.5 kgs. The difference between that average and Joe's weight is 5.5 kgs (A)