Cricket Based Problems on Average (Part 1)

Duration: 8 min

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AI Summary

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This educational video is a lecture on solving average-related problems in quantitative aptitude, presented by an instructor named Yash Jain Sir. The video begins with a problem about MS Dhoni's cricket average, where his average over 11 innings is unknown, he scores 129 runs in his 12th inning, and his average increases by 9 runs. The instructor sets up the problem using algebra, defining the initial average as 'x' and the total runs for 11 innings as '11x'. He then forms the equation for the new average: (11x + 129) / 12 = x + 9. The solution is shown step-by-step, leading to the conclusion that the initial average was 21. The video then transitions to a second problem about Virat Kohli, where he scores 30 more runs than the average of the other 6 batsmen, and the total runs scored by all 7 batsmen is 310. The instructor again uses algebra, setting the average of the other 6 batsmen as 'x', so Kohli's score is 'x+30'. The equation becomes 6x + (x+30) = 310, which simplifies to 7x = 280, giving x = 40. The final answer for Kohli's score is 70. The lecture uses a blackboard format with clear, handwritten equations and includes a brief conceptual explanation that the average is a 'sharing' of values from the highest to the lowest.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card displaying the word 'AVERAGE' in a futuristic, glowing green font against a dark, digital background. It then transitions to a lecture format where the instructor, Yash Jain Sir, introduces the first problem. The problem, labeled Q1, is displayed on a digital blackboard: 'MS Dhoni has definite average of 11 innings. He scored 129 runs in 12th inning and the average of his runs increased by 9 runs. What is the average of his 11 innings?'. The options are (a) 17, (b) 21, (c) 29, (d) Data Insufficient. The instructor begins to solve the problem by setting the average of the first 11 innings as 'x'. He writes 'Avg = x' and 'Sum = 11x' on the board, establishing the initial conditions for the problem.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to solve the first problem. He writes the equation for the new average after the 12th inning: (Sum of 11 innings + 129) / 12 = (Average of 11 innings + 9). This translates to (11x + 129) / 12 = x + 9. He then multiplies both sides by 12 to eliminate the denominator, resulting in 11x + 129 = 12(x + 9). He expands the right side to 12x + 108. The equation becomes 11x + 129 = 12x + 108. He then rearranges the terms to isolate x, subtracting 11x from both sides to get 129 = x + 108. Finally, he subtracts 108 from both sides, yielding x = 21. The instructor concludes that the average of his 11 innings is 21, which corresponds to option (b).

  3. 5:00 – 7:44 05:00-07:44

    The video transitions to the second problem, Q2, which is about Virat Kohli. The problem states: 'The captain of India Cricket Team, Virat Kohli, scored 30 more runs than the average run of other 6 batsman of his team. If total 310 runs scored by all the batsman then the runs scored by Captain Kohli is _?'. The options are (a) 50, (b) 60, (c) 70, (d) 80. The instructor sets the average of the other 6 batsmen as 'x', so their total runs are 6x. Kohli's score is then 'x + 30'. The total runs for all 7 batsmen is 6x + (x + 30) = 310. He simplifies this to 7x + 30 = 310, then 7x = 280, and finally x = 40. The score of Kohli is x + 30 = 40 + 30 = 70. The instructor confirms the answer is (c) 70. The video ends with a 'THANKS FOR WATCHING' screen.

The video presents a structured lesson on solving average problems using algebra. It begins with a problem where a new score changes the overall average, demonstrating how to set up and solve a linear equation. The core concept is that the total sum of values is the product of the average and the number of values. The second problem applies a similar principle but with a different structure, where one value is defined relative to the average of a group. The instructor effectively uses a step-by-step, algebraic approach to solve both problems, reinforcing the fundamental relationship between sum, average, and count.