Raju has a certain average for 9 innings. In the tenth inning, he score 100 runs thereby increasing his average by 8 runs. Now, his average will be

1. A

   20

2. B

   21

3. C

   28

4. D

   32

Appeared in: UPPSC 2022

Explanation

• The problem requires finding the new average after a new score is added, which changes the average by a known amount.
• Let the original average for 9 innings be 'x'. The total runs are 9x.
• After scoring 100 runs in the 10th inning, the new total is 9x + 100 for 10 innings.
• The new average is (9x + 100)/10. This is also given as the old average plus 8, i.e., x + 8.
• Solving the equation (9x + 100)/10 = x + 8 gives x = 20, which is the old average.
• The new average is the old average plus the increase: 20 + 8 = 28.

Why Other Options Were Wrong

• Option A: This value represents the original average for the first 9 innings, not the new average after the 10th inning.
• Option B: This is a calculation error and does not logically result from the data provided in the problem.
• Option D: This value may result from incorrectly adding the increase of 8 to the new average (28 + 8 = 36, which is not 32) or another miscalculation.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of arithmetic mean (average) and solving algebraic equations as background academic context rather than a clinical decision trigger.
• Calculating averages is a fundamental mathematical skill tested in the general aptitude section of nursing entrance exams.
• This type of problem assesses logical reasoning and the ability to translate a word problem into a mathematical equation, a skill useful in many clinical calculations.
• What if the average had decreased by 2 runs? The equation would be (9x + 100)/10 = x - 2. Solving this gives x = 120, and the new average would be 118.

How to Approach the Question

• First, identify the knowns and unknowns. Knowns: initial innings (9), new score (100), increase in average (8). Unknown: initial average.
• Represent the unknown initial average with a variable, such as 'x'.
• Formulate an expression for the total runs before the 10th inning (9x) and after (9x + 100).
• Set up an equation by equating the two ways of expressing the new average: (Total Runs / Total Innings) = (Old Average + Increase). This gives (9x + 100)/10 = x + 8.
• Solve the algebraic equation for 'x' to find the original average.
• Carefully read the question again to ensure you are providing the value it asks for (the new average), not the original average you just solved for.

Concept Tested & Keywords

• Concept Tested: Calculation of arithmetic mean (average) and solving algebraic equations.
• Stem keywords: average, 9 innings, tenth inning, 100 runs, increasing average, 8 runs
• Lead-in keywords: average will be

Question ID

QK8DRnLK9UVSksd8FgIsfX

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Reference Book

E6 NursingResearch Sukhpal Kaur p. 441-443