The average weight of three men A, B and C is 84 kg. Another man D joins the group and the average weight of the four men becomes 80 kg. Then another man E, whose weight is 3 kg more than that of D, replaces A. The average weight of B, C, D and E now becomes 79 kg. What is the weight of A?

Introduction / Context:
This problem focuses on average weight and how it changes when people join or leave a group. It is a multi-step average problem where you need to track totals and substitutions carefully. Such questions are common in aptitude tests to check your control over algebraic expressions and averages when several conditions are given in sequence.

Given Data / Assumptions:

Average weight of A, B and C = 84 kg.
Average weight of A, B, C and D = 80 kg.
Weight of E is 3 kg more than the weight of D.
After E replaces A, the average weight of B, C, D and E = 79 kg.
All weights are in kilograms; we assume no other changes in membership apart from what is stated.

Concept / Approach:
The key is to convert each average into an equation involving total weights. For each group, total weight = average * number of people. We first use the averages to find the total weight of A, B, C and the weight of D. Then we use the second condition involving B, C, D and E to find B + C and then isolate A by subtraction. Systematic manipulation of these totals leads directly to the required weight of A.

Step-by-Step Solution:
Step 1: Compute the total weight of A, B and C. A + B + C = 84 * 3 = 252 kg. Step 2: Use the second average to find D. (A + B + C + D) / 4 = 80, so A + B + C + D = 320. Substitute A + B + C = 252 to get 252 + D = 320, so D = 68 kg. Step 3: Express E in terms of D. E = D + 3 = 68 + 3 = 71 kg. Step 4: Use the third average involving B, C, D and E. (B + C + D + E) / 4 = 79, so B + C + D + E = 316. Substitute D = 68 and E = 71 to get B + C + 68 + 71 = 316. So B + C + 139 = 316, hence B + C = 177. Step 5: Find A. From A + B + C = 252 and B + C = 177, we get A = 252 - 177 = 75 kg.

Verification / Alternative Check:
With A = 75, B + C = 177, so A + B + C = 252 and average of A, B, C is 252 / 3 = 84 kg as given. Adding D = 68 gives 320, giving average 80 kg for A, B, C, D. Replacing A by E = 71 gives B + C + D + E = 177 + 68 + 71 = 316 and average 79 kg, matching all conditions. This confirms that A = 75 kg is correct.

Why Other Options Are Wrong:
70 kg or 72 kg would change the total of A, B and C, making it impossible to satisfy all three average conditions simultaneously.
80 kg would make A too heavy and would push earlier averages above the given values once the other weights are fixed by the equations.

Common Pitfalls:
Many students attempt to solve by guessing weights rather than forming equations, which is unreliable. Another common mistake is forgetting that replacing a member affects which people are included in the final average. Mixing up totals for three-person and four-person groups can also cause errors. Writing down each equation clearly and solving step by step avoids these issues.

Final Answer:
The weight of A is 75 kg.