In the first 20 overs of a cricket game, the run rate was 6.2. What should be the run rate in the next 30 overs to reach the target of 360 runs?

Appeared in: DSSSB - 29 August 2019 (Shift-1)

Explanation

First, calculate the total runs scored in the initial 20 overs by multiplying the overs by the run rate: 20 overs × 6.2 runs/over = 124 runs.
Next, determine the number of runs still needed to reach the target by subtracting the scored runs from the target: 360 runs - 124 runs = 236 runs.
Finally, calculate the required run rate for the remaining 30 overs by dividing the needed runs by the remaining overs: 236 runs ÷ 30 overs = 7.866... runs/over.
Rounding the result to two decimal places gives 7.87, which is the necessary average score per over to achieve the target.

Option A: A run rate of 7.92 would result in scoring 237.6 runs (7.92 × 30), which is more than the 236 runs needed. This is a result of a minor calculation error or incorrect rounding.
Option B: A run rate of 8.02 is significantly higher than required. It would lead to scoring 240.6 runs (8.02 × 30), overshooting the target by nearly 5 runs.
Option D: A run rate of 7.66 is too low. It would only yield 229.8 runs (7.66 × 30), causing the team to fall short of the 236-run requirement by about 6 runs.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of required run rate in a limited-overs game as background academic context rather than a clinical decision trigger.
Although this is a mathematics question, the underlying skill of accurate calculation is fundamental in nursing for tasks like medication dosage, IV drip rate settings, and fluid balance monitoring.
Errors in calculation can have severe patient safety consequences, highlighting the need for precision and double-checking, much like how miscalculating a run rate leads to an undesirable outcome in a game.
What if? - If the target was 330 runs instead of 360, the required runs would be 330 - 124 = 206. The new required run rate would be 206 ÷ 30 = 6.87 runs per over, showing how a single variable change impacts the entire calculation.

How to Approach the Question

First, identify all the given numerical values: initial overs (20), initial run rate (6.2), remaining overs (30), and the final target score (360).
Break the problem down into a sequence of smaller, manageable calculations. The first logical step is to determine how many runs have already been scored.
Next, calculate the difference between the target score and the runs already scored to find out how many more runs are needed.
Finally, use the number of remaining overs to calculate the required rate (average) by dividing the runs needed by the overs left.
Perform the division and round your answer to match the format of the options provided, then select the corresponding choice.

Concept Tested & Keywords

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Practise the full DSSSB - 29 August 2019 (Shift-1)

Attempt every question from this paper in a timed mock, then review the full solution for each one.