Question

The average score of Sehwag in 10 innings was 77 runs. In the s. \(11^{\text {th }}\) innings he had scored zero runs. The overall average score of Sehwag in all the 11 innings was : (a) 77 (b) \(7.7\) (c) 11 (d) none of these

Short answer

a) 77 b) 75 c) 76 d) none of these Answer: d) none of these

Step-by-step solution

Find the total runs in the first 10 innings

Since the average score in the 10 innings is 77, we can find the total runs by multiplying the average score by the number of innings: Total runs in 10 innings = Average score × Number of innings = 77 × 10

Calculate the total runs in all 11 innings

We are given that Sehwag scored zero runs in the 11th inning. So, the total runs in all the 11 innings will be the same as the total runs in the first 10 innings: Total runs in 11 innings = 77 × 10 (since 0 runs were scored in the 11th inning)

Find the overall average score in 11 innings

To find the overall average score in 11 innings, we will divide the total runs in 11 innings by the number of innings: Overall average score = Total runs in 11 innings ÷ Number of innings = (77 × 10) ÷ 11

Evaluate the expression and choose the correct answer

Now we can evaluate the expression to find the overall average score: Overall average score = (770) ÷ 11 = 70 Since the overall average score in 11 innings is 70, the correct answer is (d) none of these.

Key concepts

Average Score Calculation

Calculating the average score in sports like cricket is a fundamental application of mathematics, assessing a player’s performance over a certain number of games, or 'innings'.

To calculate the average score, you must first determine the total runs scored over all innings, and then divide this figure by the number of innings played. It's important to include all innings played, even if the score in an inning is zero, as it affects the overall average. For example, if Sehwag scored an average of 77 runs over 10 innings, the total runs scored would be the average (77) multiplied by the number of innings (10), resulting in 770 runs.

In the event that the next inning scored zero runs, the total remains 770 runs, but this total is now divided by 11 to find the new average after the 11th inning. This crucial step reflects the impact of a no-score inning on a player's average. Understanding this process is pivotal for anyone interested in sports statistics or looking to improve their quantitative aptitude.

Quantitative Aptitude

Quantitative aptitude refers to the ability to handle numbers and carry out various mathematical operations efficiently. It encompasses a wide range of skills including arithmetic, algebra, geometry, and data interpretation.

Developing a strong quantitative aptitude is essential for solving problems in a methodical manner. In the context of cricket averages, it implies an understanding of fundamental operations such as multiplication for total runs and division for calculating averages.

For students and professionals alike, quantitative aptitude is indispensable. It enhances logical reasoning and analytical thinking, allowing individuals to approach complex problems in a structured way. It's often assessed in competitive exams and aptitude tests, making it a critical area for academic and career development.

Problem Solving

Problem solving is a critical skill that involves understanding the problem at hand, identifying the relevant information, devising a plan, and executing that plan to arrive at a solution. It's not only about finding the answer but also about comprehending the process that leads to the solution.

When solving the problem of finding Sehwag's average after 11 innings, the problem solver needs to carefully perform each step: determining total runs, adjusting average calculations, and ensuring careful division. The application of these steps showcases systematic problem-solving skills.

Moreover, effective problem solving requires attentive reading to identify that a zero score still counts as an inning—frequently missed details can lead to incorrect conclusions. Through practice, anyone can enhance their problem-solving abilities, enabling them to tackle mathematical challenges and real-life scenarios with confidence and precision.