In a 50 over one day cricket match, Team A scores at an average of 4.5 runs per over for the first 30 overs and 5.5 runs per over for the remaining 20 overs. Team B plays the full 50 overs while chasing and loses by 10 runs. What is the average runs per over scored by Team B?

Introduction / Context:
This is a cricket run rate comparison problem. Team A scores at two different average rates in different phases of its innings. Team B then bats the full 50 overs while chasing this total and falls short by 10 runs. You must calculate Team B average scoring rate. Such questions combine average calculations, total runs and a comparison between two teams performance.

Given Data / Assumptions:
- Total overs in the match for each team = 50 overs.
- Team A scores at 4.5 runs per over in the first 30 overs.
- Team A scores at 5.5 runs per over in the remaining 20 overs.
- Team B plays all 50 overs and loses by 10 runs.
- We must find the average runs per over scored by Team B.

Concept / Approach:
The first step is to determine Team A total score using the given run rates for the two segments of its innings. Once we know this total, Team B score must be 10 runs less because it loses by 10 runs. Dividing Team B total runs by 50 overs gives the average runs per over scored by Team B. The entire solution uses only basic average and multiplication operations.

Step-by-Step Solution:
Step 1: Runs scored by Team A in the first 30 overs = 30 * 4.5.Step 2: Calculate this: 30 * 4.5 = 135 runs.Step 3: Runs scored by Team A in the remaining 20 overs = 20 * 5.5.Step 4: Calculate this: 20 * 5.5 = 110 runs.Step 5: Total runs scored by Team A = 135 + 110 = 245 runs.Step 6: Team B loses by 10 runs, so Team B total score = 245 - 10 = 235 runs.Step 7: Team B plays all 50 overs, so average runs per over for Team B = 235 / 50.Step 8: Compute the average: 235 / 50 = 4.7 runs per over.Step 9: Therefore, Team B average scoring rate is 4.7 runs per over.

Verification / Alternative check:
To check, multiply Team B average by total overs: 4.7 * 50 = 235. Since Team A scored 245 runs, Team B is indeed 10 runs short, confirming the match result described. Also note that Team B average is slightly higher than Team A early run rate of 4.5 but lower than Team A later run rate of 5.5, which is reasonable for a chasing effort that falls slightly short.

Why Other Options Are Wrong:
An average of 5.2 runs per over would give Team B a total of 5.2 * 50 = 260 runs, which would win the match instead of losing by 10 runs. Similarly, 4.4 or 4.6 runs per over would produce totals of 220 or 230 runs, which do not match the given margin of defeat. Only 4.7 runs per over corresponds exactly to a total of 235 runs and a 10 run loss against 245.

Common Pitfalls:
Some students mistakenly average the two run rates of Team A without considering the number of overs in each segment, or they try to average Team A and Team B run rates directly. Others forget to subtract 10 from Team A total to get Team B score. Always compute exact totals from the given averages and then apply the stated winning margin to determine the chasing team total.

Final Answer:
Team B scored at an average rate of 4.7 runs per over.