In the first 45 overs of a 50-over cricket innings, the run rate was 5.8 runs per over. What run rate is required in the remaining overs so that the team reaches a total of 295 runs?

Introduction / Context:
This is a run rate problem in a limited overs cricket match. We know the scoring rate for an initial block of overs and the total target runs. The task is to compute the required run rate in the remaining overs so that the team can reach the target score exactly by the end of the innings.

Given Data / Assumptions:

• Total overs in the innings = 50.
• Overs already completed = 45.
• Run rate in the first 45 overs = 5.8 runs per over.
• Target total runs to be achieved = 295 runs.
• We assume the team continues to bat for the full 50 overs.

Concept / Approach:
We apply two main ideas:

• Runs scored = run rate * number of overs.
• Remaining runs required = target runs minus runs already scored.
• Required run rate = remaining runs / remaining overs.

First we will compute runs scored in the first 45 overs, then determine how many runs are needed from the last 5 overs, and finally compute the required average run rate for those overs.

Step-by-Step Solution:
Step 1: Compute runs scored in first 45 overs. Runs scored = run rate * overs = 5.8 * 45. 5.8 * 45 = (5.8 * 40) + (5.8 * 5) = 232 + 29 = 261 runs. Step 2: Compute remaining runs to reach 295. Remaining runs = target - already scored = 295 - 261 = 34 runs. Step 3: Compute remaining overs. Total overs = 50, overs used = 45, so remaining overs = 5. Step 4: Compute required run rate. Required run rate = remaining runs / remaining overs. Required run rate = 34 / 5 = 6.8 runs per over.

Verification / Alternative check:
If the team scores at 6.8 runs per over for the last 5 overs, it will score 6.8 * 5 = 34 runs in those overs. Adding this to the 261 runs already scored gives 261 + 34 = 295, which matches the target total. The computation is straightforward and consistent, confirming the required rate.

Why Other Options Are Wrong:
A required run rate of 6.9 would yield 6.9 * 5 = 34.5 runs, slightly overshooting the target. A rate of 6.7 gives 33.5 runs, leaving the team short, and 6.6 gives only 33 runs, also short. Only 6.8 runs per over gives exactly 34 runs in 5 overs, making the final total exactly 295.

Common Pitfalls:
Some students mistakenly recalculate an overall run rate for all 50 overs instead of focusing on the remaining overs. Others may round prematurely or compute 45 * 5.8 incorrectly. The safest approach is to first find the runs scored so far, then subtract from the target to get the remaining runs, and then divide by the number of overs left to obtain the required run rate.

Final Answer:
The required run rate in the remaining overs is 6.8 runs per over.