A batsman makes a score of $84$ runs in the 21st inning and thus increases his average by $2$ runs. His average after 21st inning is

### Concept & Logic The batting average is mathematically defined as the total runs scored divided by the number of innings played. $$ \text{Batting Average} = \frac{\text{Total Runs}}{\text{Total Innings}} $$ ### Step-by-Step Solution * **Given:** * Score in the 21st inning = $84$ * Increase in overall average = $2$ * **Calculation:** Let the average after 20 innings be $x$. Total runs after 20 innings = $20x$ Total runs after 21 innings = $20x + 84$ New average after 21 innings = $x + 2$ Since the total runs after 21 innings can also be expressed as $21(x + 2)$, we set up the equation: $$ 20x + 84 = 21(x + 2) $$ $$ 20x + 84 = 21x + 42 $$ $$ x = 42 $$ The question specifically asks for the average *after* the 21st inning, which is $x + 2$. $$ 42 + 2 = 44 $$ ### Exam Strategy & Shortcut You can solve this mentally in under 10 seconds. The batsman increased his average by $2$ runs over $21$ innings. This means he needed $21 \times 2 = 42$ extra runs above his old average to pull the overall average up by $2$. Old Average = Runs scored - Extra runs = $84 - 42 = 42$. New Average = Old Average + $2 = 42 + 2 = 44$. ### Common Pitfall The most frequent mistake is stopping at solving for $x = 42$ and selecting that as the answer. Always re-read the final sentence of the question to ensure you are finding the "new" average, not the previous one. ### Final Answer **Therefore, the correct answer is 44.**