Short Trick to Find Selling Price Quickly

Duration: 12 min

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AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video is a tutorial on solving profit and loss problems, presented by a teacher from Knowledge Gate. The video begins with a problem where a person, Jethalal, sells an item for Rs. 720 and incurs a 25% loss, and the task is to find the selling price for a 25% gain. The instructor first uses a 'Trick 1' method, calculating the cost price (CP) as 720 / 0.75 = Rs. 960, and then the new selling price (SP) as 960 * 1.25 = Rs. 1200. He then demonstrates a 'Trick 2' method, which involves setting the CP as 100% and using the ratio of SP to CP to find the new SP. The video then transitions to a second problem: if the cost price of 36 books equals the selling price of 30 books, what is the gain or loss percentage? The instructor solves this using a 'Conventional Method' by assuming a cost price of 'x' per book, leading to a gain of 20%. He then shows a 'Short Trick' method, where the ratio of CP to SP is 30:36, which simplifies to 5:6, directly yielding a 20% gain. The video concludes with a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card for a problem: 'Q1: If Jethalal has to sell an electronic item for Rs. 720, he would lose 25%. In order to gain 25%, he should sell it for ??'. The instructor, Yash Jain, introduces the problem. The screen then transitions to a green chalkboard where the instructor begins to solve the problem using 'Trick 1'. He writes the formula for cost price (CP) as 720 / (1 - 0.25) and the formula for the new selling price (SP) as CP * (1 + 0.25). He also writes the formula for loss (L) as CP - SP and the formula for profit (P) as SP - CP.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to solve the first problem on the green chalkboard. He calculates the cost price (CP) as 720 / 0.75, which equals 960. He then calculates the new selling price (SP) for a 25% gain as 960 * 1.25, which equals 1200. He writes the final answer as SP = 1200. The instructor explains that the cost price is 960, and to gain 25%, the selling price should be 1200. He also writes the formula for loss percentage as (Loss / CP) * 100 and the formula for profit percentage as (Profit / CP) * 100.

  3. 5:00 – 10:00 05:00-10:00

    The instructor introduces 'Trick 2' for the first problem. He sets the cost price (CP) as 100%. He then calculates the selling price (SP) for a 25% loss as 75% of CP, which is 720. He uses the ratio 75:100 = 720:CP to find CP, which is 960. He then calculates the new SP for a 25% gain as 125% of CP, which is 1200. He writes the final answer as SP = 1200. The instructor explains that the cost price is 960, and to gain 25%, the selling price should be 1200. He also writes the formula for loss percentage as (Loss / CP) * 100 and the formula for profit percentage as (Profit / CP) * 100.

  4. 10:00 – 12:02 10:00-12:02

    The video transitions to a new problem: 'Q2: The cost price of 36 books is equal to selling price of 30 books. The gain or loss % is __'. The instructor introduces the 'Conventional Method'. He assumes the cost price of one book is 'x'. Therefore, the cost price of 36 books is 36x. The selling price of 30 books is also 36x, so the selling price of one book is 36x/30 = 1.2x. He calculates the profit as SP - CP = 1.2x - x = 0.2x. He then calculates the profit percentage as (0.2x / x) * 100 = 20%. He writes the final answer as 20%. The instructor then introduces the 'Short Trick' method, where the ratio of CP to SP is 30:36, which simplifies to 5:6, directly yielding a 20% gain. The video ends with a 'Thanks for Watching' screen.

The video provides a comprehensive tutorial on solving profit and loss problems using two distinct methods. The first problem demonstrates how to find a new selling price given a loss and a desired gain, using both a direct calculation method and a ratio-based method. The second problem illustrates how to find the gain percentage when the cost price of a certain number of items is equal to the selling price of a different number, using both a conventional algebraic approach and a more efficient 'short trick' based on ratios. The core concept is that profit and loss are calculated based on the cost price, and the key to solving these problems efficiently lies in understanding the relationship between cost price, selling price, and the percentage change.

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