A batsman in his 14th innings makes a score of 86 runs and thereby increasing his average by 3 runs. What is his average (in runs) after the 14th innings?

1. A

   86

2. B

   50

3. C

   89

4. D

   47

Appeared in: Bihar NHM CHO-2025

Explanation

• The question asks for the new average after the 14th innings, which is 3 more than the previous average.
• Let the average after 13 innings be 'x'. The total runs scored in these innings is 13x.
• After scoring 86 runs in the 14th innings, the total runs become 13x + 86.
• The new average after 14 innings is the total runs divided by 14, which is (13x + 86) / 14.
• We are given that the new average is also x + 3. By equating the two expressions for the new average, we get the equation: (13x + 86) / 14 = x + 3.
• Solving this equation for x gives x = 44. This is the average before the 14th innings.

Why Other Options Were Wrong

• Option A: This is the score the batsman made in the 14th innings, not his average after 14 innings.
• Option B: This value does not result from the correct calculation. It might be a random guess or the result of a significant calculation error.
• Option C: This value does not result from the correct calculation. It could be a miscalculation, possibly from incorrectly adding or subtracting values.

Related Visual

• Visual 1: Flowchart - A step-by-step flowchart illustrating the algebraic method to solve for the new average, starting from defining the variable 'x' to the final calculation.
• Visual 2: Infographic - An infographic explaining the shortcut method. It would visually show the 86 runs, with a portion (42 runs) being distributed across the 14 innings (3 runs each) and the remaining portion (44 runs) representing the old average.

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) in a real-world scenario as background academic context rather than a clinical decision trigger.
• This question tests general quantitative aptitude and problem-solving skills, which are essential for nurses.
• While not a direct clinical calculation, the logical reasoning required is similar to that used in tasks like medication dosage calculation and interpreting patient data trends.
• What if the average had decreased by 3 runs? The equation would be 13x + 86 = 14(x - 3). This would lead to 13x + 86 = 14x - 42, so x = 128. The new average would be 128 - 3 = 125.

How to Approach the Question

• First, carefully read the question to identify all the given information: initial number of innings (13), final number of innings (14), score in the 14th inning (86), and the increase in average (3).
• Define an algebraic variable, such as 'x', to represent the unknown quantity, which is the average after 13 innings.
• Formulate an equation based on the definition of average: Average = (Total Sum) / (Number of items).
• Express the total runs after 14 innings in two different ways: (Total runs from 13 innings + Score in 14th inning) and (14 * New average).
• Set up the equation: 13x + 86 = 14(x + 3).
• Solve the linear equation for 'x'. Remember that 'x' is the old average.

Concept Tested & Keywords

• Concept Tested: Calculation of arithmetic mean (average) in a real-world scenario.
• Stem keywords: batsman, 14th innings, score, 86 runs, average, increasing by 3 runs
• Lead-in keywords: What is

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