Water mixed to a mixture & sold at CP to make profit (2)

Duration: 10 min

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AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video presents a lecture on the 'Alligation Method' for solving mixture and profit problems, a common topic in competitive exams. The instructor, Yash Jain, begins by introducing the topic with a title slide. He then presents two distinct problems. The first problem asks for the ratio of water to alcohol to be mixed so that a 22.5% profit is made when the mixture is sold at the cost price of the alcohol. The second problem asks for the ratio of water to milk to gain a 16.66% profit when the mixture is sold at the cost price of milk. For both problems, the instructor uses the alligation method, which involves setting up a diagram to find the ratio of the cheaper and dearer components. He demonstrates the method by first calculating the mean price using the formula: Mean Price = CP * (100 / (100 + P)), where CP is the cost price and P is the profit percentage. He then applies the alligation rule: (Dearer - Mean) : (Mean - Cheaper) to find the required ratio. The video concludes with a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with an animated title card featuring a scientist in a lab, with the word 'MIXTURE' displayed at the bottom. This transitions to a presentation slide with a geometric background. The slide is titled 'MIXTURES & ALLIGATIONS' and is attributed to 'Yash Jain'. A small video window in the bottom right corner shows the instructor, Yash Jain, speaking. The slide also contains a copyright notice for 'KNOWLEDGE GATE EDUVENTURES'. The instructor introduces the topic of mixtures and alligations, setting the stage for the lesson.

  2. 2:00 – 5:00 02:00-05:00

    The first problem is presented on the slide: 'Que: In what ratio water and alcohol be mixed so that even after selling the mixture at Cost Price, a profit of 22.5% is received?'. The instructor begins to solve this by setting the cost price (CP) of alcohol to 10 and the selling price (SP) to 10, as the mixture is sold at the cost price of the alcohol. He then calculates the profit percentage (P) as 22.5%. He writes the formula for the mean price: 'Mean Price = CP (100 / (100 + P))'. He substitutes the values, writing '10 (100 / (100 + 22.5))', which simplifies to '10 (100 / 122.5)'. He then converts 122.5 to a fraction, writing '10 (100 / (245/2))', which simplifies to '10 (200 / 245)'. He further simplifies this to '10 (40 / 49)'. The instructor then begins to set up the alligation diagram, writing '0' for the cost price of water and '10' for the cost price of alcohol.

  3. 5:00 – 9:38 05:00-09:38

    The instructor completes the alligation diagram for the first problem. He writes the mean price as '400/49' and the cost prices as '0' and '10'. He calculates the differences: '10 - 400/49 = 90/49' and '400/49 - 0 = 400/49'. The ratio is then (90/49) : (400/49), which simplifies to 90:400 or 9:40. He concludes that the ratio of water to alcohol is 9:40. He then moves to the second problem: 'Que: In what ratio must water be mixed with milk to gain 16.66% on selling the mixture at cost price?'. He sets the cost price of milk (CP) to 10 and the profit (P) to 16.66%, which he writes as 50/3. He calculates the mean price as '10 (100 / (100 + 50/3))', which simplifies to '10 (300 / 350)' or '10 (6/7)'. He writes the mean price as '60/7'. He sets up the alligation diagram with '0' for water and '10' for milk. He calculates the differences: '10 - 60/7 = 10/7' and '60/7 - 0 = 60/7'. The ratio is (10/7) : (60/7), which simplifies to 10:60 or 1:6. He concludes that the ratio of water to milk is 1:6. The video ends with a 'THANKS FOR WATCHING' screen.

The video provides a clear, step-by-step demonstration of the alligation method for solving mixture problems. It begins by establishing the core concept: when a cheaper substance (like water) is mixed with a dearer one (like alcohol or milk), the profit is achieved by selling the mixture at the cost price of the dearer substance. The instructor systematically applies the formula for mean price and the alligation rule to two different scenarios. The key learning point is the methodical approach to setting up the alligation diagram, which visually represents the relationship between the cost prices of the components and the mean price of the mixture, allowing for the direct calculation of the required ratio.

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