The average weight of two football players P and Q is 38 kg. The average weight of P, Q and their coach T is 49 kg. What is the weight (in kg) of the coach T?

Introduction / Context:
This is a simple average and total weight problem involving two players and their coach. The question checks whether you can move between averages and totals and use the difference in group sizes to find the coach's weight.

Given Data / Assumptions:
- Average weight of P and Q = 38 kg. - Average weight of P, Q and coach T = 49 kg. - We assume weights are in kilograms. - We need to find the weight of the coach T.

Concept / Approach:
Average weight of a group is equal to total weight of the group divided by number of persons. From the first average, we can get the total weight of P and Q. From the second average, we can get the total weight of P, Q and T together. The difference between these two totals equals the weight of the coach T. This is a straightforward application of the average formula.

Step-by-Step Solution:
Step 1: Average weight of P and Q = 38 kg. Step 2: Number of players in this group = 2. Step 3: Total weight of P and Q = 38 * 2 = 76 kg. Step 4: Average weight of P, Q and T together = 49 kg. Step 5: Number of persons in this group = 3. Step 6: Total weight of P, Q and T = 49 * 3 = 147 kg. Step 7: Weight of coach T = total of P, Q and T minus total of P and Q. Step 8: Weight of T = 147 - 76 = 71 kg.

Verification / Alternative check:
Substitute back to verify. If T weighs 71 kg, total weight of P and Q is 76 kg, so total for all three is 76 + 71 = 147 kg. Average for all three = 147 / 3 = 49 kg, which matches the given data. Average of P and Q remains 76 / 2 = 38 kg, also correct. Thus the value 71 kg is fully consistent.

Why Other Options Are Wrong:
Option B (46 kg): Would give total weight 76 + 46 = 122 kg, giving an average of 122 / 3, not equal to 49 kg. Option C (76 kg): Then total would be 76 + 76 = 152 kg, with an average greater than 49 kg. Option D (91 kg): Would make the average too high as well. Option E (68 kg): Also fails to produce an average of 49 kg for three persons.

Common Pitfalls:
A common mistake is to average the two averages (38 and 49) or to subtract them directly and assume the result is related to the coach's weight. Another error is to forget to multiply the averages by the number of persons to get the totals. The correct approach is always to compute totals first, then use differences of totals to isolate the unknown weight.

Final Answer:
The weight of coach T is 71 kg.