Find Overall Profit & Loss Percentage

Duration: 7 min

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AI Summary

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This educational video presents a tutorial on solving profit and loss problems, a common topic in competitive exams. The instructor, Yash Jain Sir from Knowledge Gate, begins by introducing a problem where a person sells two items at the same selling price, making a 10% profit on one and a 10% loss on the other, and asks for the overall profit or loss percentage. He then demonstrates a 'short trick' method to solve this, using the formula for overall loss percentage: (Profit/Loss %)^2 / 100. The video then transitions to a second problem involving two cycles sold at the same price, with a 20% profit on one and a 20% loss on the other, and an overall loss of Rs. 18. The instructor uses the same method to find the difference in the cost prices of the two cycles. The lesson is delivered through a combination of on-screen text, a green chalkboard for calculations, and a live video feed of the instructor.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card showing a 3D figure on a balance scale with the words 'PROFIT' and 'LOSS'. It then transitions to a lecture format. The instructor, Yash Jain Sir, introduces the first problem (Q1) displayed on the screen: 'A person on selling 2 match stick boxes at the same rate gains profit of 10% on 1 box and 10% loss on other box. Find the overall profit % or loss %?'. The problem is noted as being from the ATOS EXAM (2018). The instructor begins to explain the concept, setting up the context for a 'short trick' to solve the problem.

  2. 2:00 – 5:00 02:00-05:00

    The instructor begins solving the first problem on a green chalkboard. He writes 'CPS' (Cost Price of Selling) and 'CLS' (Cost Price of Loss) to represent the two items. He then writes the formula for profit: 'P = 10 = 1/10', and for loss: 'L = 10 = 1/10'. He explains that the selling price is the same for both items. He uses the 'short trick' formula for overall loss percentage: (Profit/Loss %)^2 / 100. He calculates (10)^2 / 100 = 100 / 100 = 1%. He concludes that the overall loss is 1%.

  3. 5:00 – 6:37 05:00-06:37

    The video transitions to the second problem (Q2), which is displayed on the screen: 'Two cycles are sold at same selling price. The first cycle is sold at 20% profit while the second cycle is sold at 20% loss, the overall loss encountered is Rs. 18, find the difference of cost price of both?'. The problem is noted as being from the JIO EXAM (2019). The instructor applies the same 'short trick' method. He uses the formula for overall loss percentage: (20)^2 / 100 = 4%. He states that this 4% loss corresponds to Rs. 18. He then calculates the total cost price (CP) as 18 / 4 * 100 = Rs. 450. He then calculates the individual cost prices: CP1 = 450 * 100 / 120 = Rs. 375 and CP2 = 450 * 100 / 80 = Rs. 562.5. Finally, he finds the difference: 562.5 - 375 = Rs. 187.5. The video ends with a 'THANKS FOR WATCHING' screen.

The video provides a clear and concise tutorial on a specific type of profit and loss problem. It demonstrates a powerful 'short trick' method for calculating the overall loss when two items are sold at the same price, one at a profit and the other at a loss. The key insight is that the overall loss percentage is the square of the individual percentage divided by 100. The instructor effectively applies this formula to two different problems, first to find the percentage loss and then to find the absolute difference in cost prices given the total loss amount. The progression from a conceptual problem to a numerical one reinforces the method's utility for competitive exam preparation.