In the first 39 overs of a cricket match, the run rate of a team was 4.6 runs per over. What run rate is required in the remaining 11 overs so that the team reaches a target of 252 runs?

Introduction / Context:
This is a run rate calculation problem from cricket, a favourite topic in quantitative aptitude. The team has already played 39 overs at a known run rate and now needs to chase a target of 252 runs. You must determine the required run rate in the remaining 11 overs so that the team can reach the target. This tests basic arithmetic with averages and a clear understanding of how run rate relates to total runs.

Given Data / Assumptions:
- Total overs in the innings = 50 overs (39 already played and 11 remaining, though the exact full quota is not strictly needed).
- Run rate in the first 39 overs = 4.6 runs per over.
- Target score = 252 runs.
- Overs already completed = 39.
- Overs remaining = 11.
- We must find the required average run rate in the last 11 overs.

Concept / Approach:
The total runs scored so far can be calculated by multiplying the run rate by the overs already bowled. The remaining runs to be scored are equal to the target minus runs already scored. Once we know how many runs remain and how many overs are left, the required run rate is simply remaining runs divided by remaining overs. This is exactly the same concept as average speed or average marks, but applied to cricket runs.

Step-by-Step Solution:
Step 1: Runs scored in the first 39 overs = 39 * 4.6.Step 2: Compute 39 * 4.6 = 39 * 46 / 10 = 1794 / 10 = 179.4 runs.Step 3: Target runs = 252, so remaining runs to be scored = 252 - 179.4.Step 4: Calculate the remaining runs: 252 - 179.4 = 72.6 runs.Step 5: Overs remaining = 50 - 39 = 11 overs.Step 6: Required run rate in the remaining overs = remaining runs / remaining overs = 72.6 / 11.Step 7: Perform the division: 72.6 / 11 = 6.6 runs per over.Step 8: Therefore, the team must score at an average of 6.6 runs per over in the last 11 overs to reach 252 runs.

Verification / Alternative check:
Multiply the required run rate back by the remaining overs: 6.6 * 11 = 72.6. Adding this to the runs already scored gives 179.4 + 72.6 = 252. This exactly matches the target score, confirming that the run rate of 6.6 runs per over is correct. Any small difference would show up immediately when you recompute the final total.

Why Other Options Are Wrong:
If the required rate were 7.2, then runs in the last 11 overs would be 7.2 * 11 = 79.2 and the final total would be 179.4 + 79.2 = 258.6, which overshoots the target. With 5.7 or 6.3 runs per over, the total runs would fall short of 252. Only 6.6 runs per over produces exactly the target score.

Common Pitfalls:
One common error is to ignore the decimal part of the run rate 4.6 and approximate it as 5, which significantly changes the calculation. Another is to forget that the target includes all runs, not just those after a certain over. Always work with the exact run rate, calculate the precise runs scored and the precise remaining runs, and then divide by the remaining overs for the required rate.

Final Answer:
The required run rate in the last 11 overs is 6.6 runs per over.