In the first 32 overs of a cricket match, the scoring rate was 7.2 runs per over. What run rate is required in the remaining 18 overs so that the team reaches a total of 297 runs?

Introduction / Context:
Run rate problems are very common in cricket-based aptitude questions. They test your understanding of averages and remaining requirement calculations. Here, you are given the scoring rate for an initial set of overs and a target total for the whole innings, and you must determine the required scoring rate in the remaining overs to reach that target.

Given Data / Assumptions:

First 32 overs have been completed.
Run rate in these 32 overs = 7.2 runs per over.
Total target score = 297 runs.
Remaining overs = 18 (since a typical limit is 50 overs, but here only the remaining 18 are relevant).
We must find the required run rate (runs per over) in these 18 overs to reach 297 runs.

Concept / Approach:
Run rate is just average runs per over. First we compute the runs already scored using the run rate in the first 32 overs. Then we subtract this from the target to find how many more runs are needed. Finally, we divide the required runs by the remaining overs to get the required run rate. Although in real matches runs are whole numbers, in aptitude problems a decimal run rate is acceptable for calculation purposes.

Step-by-Step Solution:
Step 1: Calculate runs scored in the first 32 overs. Runs scored = run rate * overs bowled = 7.2 * 32. 7.2 * 32 = 230.4 runs (mathematically, this is the product used for further calculation). Step 2: Find runs still required. Target score = 297 runs. Required runs = 297 - 230.4 = 66.6 runs. Step 3: Compute required run rate in the remaining 18 overs. Required run rate = required runs / remaining overs. Required run rate = 66.6 / 18 ≈ 3.7 runs per over.

Verification / Alternative Check:
If the team scores at 3.7 runs per over for 18 overs, it will score approximately 3.7 * 18 = 66.6 runs in those overs. Adding this to 230.4 gives total runs of about 297. The small decimal remainder is due to the decimal nature of the initial run rate, but for exam purposes, 3.7 is the appropriate required rate and matches the option given.

Why Other Options Are Wrong:
4.3 or 4.9 runs per over would yield totals well above 297 when added to the initial runs, overshooting the target.
3.1 runs per over is too low and would not allow the team to reach 297; it would leave them short of the target.

Common Pitfalls:
One frequent mistake is to round intermediate values too early or to assume that 7.2 runs per over for 32 overs must give a whole number of runs. Another error is to average the initial run rate and some guess of the final run rate instead of calculating the required rate from remaining runs and overs. Always calculate runs already scored, subtract from target, then divide by remaining overs.

Final Answer:
The team must score at a rate of approximately 3.7 runs per over in the remaining 18 overs.