Ajit has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing the average by 8 runs. His new average is?

Appeared in: NCL (MP) Nursing Officer - 2020

Explanation

Let the initial average for 9 innings be 'A'. The total runs scored in these innings is 9A.
After scoring 100 runs in the 10th inning, the new total runs become 9A + 100.
The new average for 10 innings is given as A + 8. Therefore, the new total runs can also be expressed as 10 * (A + 8).
By equating the two expressions for the total runs (9A + 100 = 10A + 80), we can solve for 'A'.
Solving the equation gives A = 20. This is the old average.
The new average is the old average plus the increase, which is 20 + 8 = 28.

Option A: The value 20 represents the old average for the first 9 innings.
Option B: This is an incorrect value that does not logically follow from the calculations.
Option D: This value is likely the result of a calculation error, possibly by adding the increase of 8 to an incorrectly calculated old average.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Problem-solving using the concept of Averages (Mean) as background academic context rather than a clinical decision trigger.
This question assesses basic mathematical aptitude and logical reasoning.
While not a clinical topic, these skills are foundational for nurses who must perform calculations for drug dosages, fluid intake/output, and interpreting patient data charts accurately.
What if the average had decreased by 8 runs? The equation would change to 9A + 100 = 10(A - 8), leading to a different outcome and highlighting the importance of careful reading.

How to Approach the Question

First, identify the knowns and unknowns in the problem: initial number of data points (9 innings), the value of the new data point (100 runs), and the change in the average (+8 runs).
Assign a variable, such as 'A', to represent the initial (old) average.
Use the fundamental formula for averages: Total = Average × Number of items.
Formulate an algebraic equation that represents the total value in two different ways: (old total + new value) and (new average × new number of items).
Solve the equation to find the value of your variable ('A'), which is the initial average.
Reread the question to ensure you are answering what is being asked (in this case, the 'new average', not the old one) and perform the final calculation.

Concept Tested & Keywords

Concept Tested: Problem-solving using the concept of Averages (Mean)
Stem keywords: average, 9 innings, tenth innings, 100 runs, increasing the average
Lead-in keywords: new average
Negative lead-in flag: false

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E6 NursingResearch Sukhpal Kaur p. 441-443

Practise the full NCL (MP) Nursing Officer - 2020

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