The average weight of 45 passengers in a bus is 52 kg. Five of them, whose average weight is 48 kg, leave the bus and another five passengers, whose average weight is 54 kg, board the bus at the same stop. What is the new average weight of the passengers in the bus?

Introduction / Context:
This problem explores how the average changes when some members leave a group and others join, each subgroup having different average weights. It is a standard type of question in aptitude exams that reinforces the idea of working with total sums and then recomputing the average after changes in group composition.

Given Data / Assumptions:

• Initial number of passengers = 45.
• Initial average weight = 52 kg.
• 5 passengers with average weight 48 kg leave the bus.
• 5 new passengers with average weight 54 kg board the bus.
• We need to find the new average weight of the passengers.

Concept / Approach:
The method is to compute the initial total weight using the initial average, adjust the total weight when some passengers leave, add the weight of the new passengers, and finally divide by the new number of passengers to get the new average. The number of passengers ends up the same (45) because 5 leave and 5 join, but the total weight changes.

Step-by-Step Solution:
Initial number of passengers = 45.Initial average weight = 52 kg.Initial total weight = 45 * 52 = 2340 kg.Five passengers with average weight 48 kg leave, so their total weight = 5 * 48 = 240 kg.Total weight after they leave = 2340 - 240 = 2100 kg.Five new passengers with average weight 54 kg board the bus, total weight of new passengers = 5 * 54 = 270 kg.New total weight = 2100 + 270 = 2370 kg.Number of passengers remains 45 (45 - 5 + 5).New average weight = 2370 / 45 = 52.666..., which is approximately 52.66 kg.

Verification / Alternative check:
The net change in total weight is the difference between the weight of the leaving group and the joining group. Leaving group weight = 240 kg, joining group weight = 270 kg, so net gain = 30 kg. Spread over 45 passengers, the average increases by 30 / 45 = 0.666..., so new average = 52 + 0.666... = 52.666..., which confirms the detailed calculation.

Why Other Options Are Wrong:
Option a (54.21 kg) and option d (53.45 kg) would require a much larger net gain in total weight than is actually happening. Option b (51.07 kg) suggests a decrease in the average even though heavier passengers replaced lighter ones. Option e (52.00 kg) assumes no change at all in total weight. Only 52.66 kg matches the exact arithmetic.

Common Pitfalls:
Some students incorrectly change the number of passengers (for example, to 40 or 50) or mis-compute the total weights of the leaving and joining groups. Others forget that the difference in subgroup averages directly affects the average of the whole group. Carefully tracking total weight and passenger count avoids these mistakes.

Final Answer:
The new average weight of the passengers in the bus is approximately 52.66 kg.