In the first 39 overs of a cricket match, the run rate 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 typical cricket run rate problem. It tests your ability to convert a given run rate into total runs scored so far and then determine the required run rate in the remaining overs to reach a specified target. Such problems are common in quantitative aptitude exams and sports based reasoning questions.

Given Data / Assumptions:
- Total overs in the innings = 50 overs (39 completed and 11 remaining). - Run rate for the first 39 overs = 4.6 runs per over. - Target runs to be scored = 252 runs. - We must find the required run rate in the last 11 overs.

Concept / Approach:
Run rate is defined as total runs scored divided by overs faced. First we compute total runs scored in the first 39 overs using the given run rate. Then we subtract this from the target to find how many runs remain to be scored. Finally, we divide the remaining runs by the remaining overs (11) to get the required run rate for those overs. This is a direct and standard application of the run rate formula.

Step-by-Step Solution:
Step 1: Compute runs scored in the first 39 overs. Step 2: Runs in first 39 overs = run rate * overs = 4.6 * 39. Step 3: Calculate 4.6 * 39. Note that 4.6 * 40 = 184, so 4.6 * 39 = 184 - 4.6 = 179.4 runs. Step 4: Total target runs = 252. Step 5: Remaining runs to be scored = target - runs already scored = 252 - 179.4. Step 6: Compute 252 - 179.4 = 72.6 runs. Step 7: Remaining overs = 50 - 39 = 11 overs. Step 8: Required run rate in the last 11 overs = remaining runs / remaining overs. Step 9: Required run rate = 72.6 / 11. Step 10: Compute 72.6 / 11 = 6.6 runs per over. Step 11: Therefore, the team must score at a run rate of 6.6 runs per over in the last 11 overs.

Verification / Alternative check:
Check the total runs if the team follows the required rate. Runs in the last 11 overs at 6.6 runs per over = 6.6 * 11 = 72.6 runs. Adding to the 179.4 runs already scored gives 179.4 + 72.6 = 252 runs, matching the target exactly. This confirms that a required run rate of 6.6 runs per over is correct.

Why Other Options Are Wrong:
Option A (7.2): Would yield more than the target when multiplied by 11 overs. Option B (5.7): Too low; it would leave the team short of 252 runs. Option C (6.3): Slightly low and would not reach the full target. Option E (7.0): Higher than required and not consistent with the exact arithmetic.

Common Pitfalls:
Mistakes often happen in the multiplication 4.6 * 39 or the division 72.6 / 11. Some may also confuse the target runs with runs still required, or use 39 instead of 11 as the denominator when computing the required run rate. Carefully keep track of what each run rate refers to and always separate runs already scored from runs yet to be scored.

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