The average weight of three persons L, M and N taken together is 93 kg. If the average weight of L and M together is 89 kg and the average weight of M and N together is 96.5 kg, what is the weight of M in kilograms?

Introduction / Context:
This is a straightforward averages and linear equations question involving the weights of three people. You are given the average of all three, as well as the averages of two different pairs. From this information, you must determine the individual weight of one person. Problems like this test your ability to convert averages to totals and then use simple algebra to isolate unknowns.

Given Data / Assumptions:
- Persons are L, M and N.
- Average weight of L, M and N together = 93 kg.
- Average weight of L and M together = 89 kg.
- Average weight of M and N together = 96.5 kg.
- We must find the weight of M in kilograms.

Concept / Approach:
The average of a group multiplied by the number of people gives the total weight of that group. We use this to find the total weights of the groups L + M + N, L + M and M + N. Then we subtract to find individual weights. Subtracting L + M from L + M + N gives N. Once N is known, we use M + N to solve for M. This is a clean and systematic way to handle such problems.

Step-by-Step Solution:
Step 1: Total weight of L, M and N = 3 * 93 = 279 kg.Step 2: Total weight of L and M = 2 * 89 = 178 kg.Step 3: Total weight of M and N = 2 * 96.5 = 193 kg.Step 4: From step 1 and step 2, find N: N = (L + M + N) - (L + M) = 279 - 178 = 101 kg.Step 5: Now use M + N = 193, so M + 101 = 193.Step 6: Solve for M: M = 193 - 101 = 92 kg.Step 7: Therefore, the weight of M is 92 kg.

Verification / Alternative check:
Check the calculation by reconstructing the averages. If M = 92 and N = 101, then L + M = 178 implies L = 178 - 92 = 86 kg. Now, L + M + N = 86 + 92 + 101 = 279 kg and 279 / 3 = 93 kg, matching the given average for all three. Also, L + M = 86 + 92 = 178 and 178 / 2 = 89, and M + N = 92 + 101 = 193 and 193 / 2 = 96.5, matching the pair averages. This confirms that the answer is consistent.

Why Other Options Are Wrong:
If M were 86, 88, 95 or 101 kg, the pair sums and averages would not match all three pieces of given information simultaneously. For example, if M were 86, then from L + M = 178 we would get L = 92, but this would not align with the value of N required to maintain the overall average of 93 kg and the given average for M and N.

Common Pitfalls:
Some students attempt to solve by guessing values rather than using totals and equations, which can be time consuming and error prone. Others confuse which totals correspond to which averages. Always compute the group totals first, subtract to get individual weights, and verify by checking all given averages at the end.

Final Answer:
The weight of M is 92 kg.