Short Trick to Find A B C given some mA = nB = pC

Duration: 5 min

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AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive tutorial on solving ratio problems involving three variables, specifically focusing on the scenario where variables are related by a common equation. The instructor, Yash Jain, explains how to find the ratio A:B:C when given an equation where the variables are multiplied by different constants, such as mA = nB = pC. The core technique involves setting the equation to a constant 'k' to isolate each variable, expressing them as fractions, and then finding the Least Common Multiple (LCM) of the denominators to simplify the result into whole numbers. This method is presented as a standard approach for competitive exams.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video begins with a title slide displaying "RATIO & PROPORTION" in bold black text next to a colorful 3D pie chart. The instructor, Yash Jain, appears in a small window and introduces the topic. A slide defines "Ratio" as "a comparison of 2 quantities," accompanied by a diagram illustrating parts and a whole. The lesson then transitions to a specific problem type titled "Finding A:B:C where mA = nB = pC". The first example problem is displayed on a yellow background: "If 3A = 5B = 6C, find A : B : C?". The instructor underlines the numbers 3, 5, and 6 to identify them as the coefficients m, n, and p.

  2. 2:00 – 5:00 02:00-05:00

    The instructor demonstrates the solution by setting the entire equation equal to a constant variable 'k', writing "3A = 5B = 6C = k". He isolates each variable to express them in terms of k: A = k/3, B = k/5, and C = k/6. He then constructs the ratio A:B:C as k/3 : k/5 : k/6. To simplify this into whole numbers, he calculates the Least Common Multiple (LCM) of the denominators 3, 5, and 6, which is 30. He multiplies each term of the ratio by 30, resulting in the final integer ratio 10 : 6 : 5. He also writes the general formula A:B:C = 1/m : 1/n : 1/p.

  3. 5:00 – 5:27 05:00-05:27

    The instructor briefly presents a second example problem: "If 2A = 3B = 4C, find A : B : C?". He applies the general formula A:B:C = 1/2 : 1/3 : 1/4. He calculates the LCM of 2, 3, and 4 as 12. Multiplying the terms by 12 yields the ratio 6 : 4 : 3. The video concludes with a black screen displaying the text "THANKS FOR WATCHING" in orange and white font.

The lesson progresses logically from basic definitions of ratio to complex algebraic applications. The key takeaway is the method of equating terms to a constant 'k' to isolate variables, followed by finding the LCM to convert fractional ratios into integers. The instructor demonstrates this with two distinct examples, reinforcing the concept that the ratio of variables is the inverse of their coefficients. This systematic approach ensures accuracy in solving ratio and proportion problems found in competitive exams, providing students with a reliable shortcut for similar questions.

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