Tricks for Comparision Based Questions

Duration: 11 min

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AI Summary

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This educational video is a lecture on solving time and work problems, a common topic in quantitative aptitude. The instructor, Yash Jain Sir, uses a digital whiteboard to present and solve three distinct problems. The first problem involves finding the time for 8 men and 12 women to complete a task, given the work rates of 4 men and 6 women in 5 days and 6 men and 4 women in 4 days. The instructor sets up equations using variables for the efficiency of a man (M) and a woman (W), equates the total work, and solves for the relationship between M and W. The second problem, from Wipro NLTH 2019, involves men and boys, where 6 men and 8 boys can complete a work in 10 days, and 26 men and 48 boys can do it in 2 days. The instructor uses a scaling method to find the work rate of 15 men and 20 boys. The third problem, from GATE ECE 2017, involves men and women building a bridge, with different combinations and timeframes. The instructor uses the concept of total work and equates the work done in different scenarios to find the number of men needed. The video concludes with a final problem on individual work rates, where the combined time for three people is calculated using the formula 1/(1/a + 1/b + 1/c). The overall teaching style is methodical, focusing on setting up equations and solving them step-by-step.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card for a 'TIME & WORK' lecture. The instructor, Yash Jain Sir, introduces the first problem (Q1) on a digital whiteboard. The problem states: '4 Men and 6 Women can do a work in 5 days. 6 Men and 4 women can do the same work in 4 days. How many days will it take to complete the work if 8 men and 12 women work together?'. The instructor begins by defining the formula for total work as 'Men * Efficiency * No. of days'. He then assigns variables: 'Let efficiency of a man be M' and 'Let efficiency of a woman be W'. He starts writing the equation for the first scenario: 'Total Work = 4M * 5 = (4M + 6W) * 5'.

  2. 2:00 – 5:00 02:00-05:00

    The instructor continues to solve the first problem. He writes the equation for the second scenario: 'Total Work = 6M * 4 = (6M + 4W) * 4'. He then equates the two expressions for total work: '(4M + 6W) * 5 = (6M + 4W) * 4'. He expands both sides: '20M + 30W = 24M + 16W'. He simplifies the equation by moving terms: '30W - 16W = 24M - 20M', which becomes '14W = 4M'. He then solves for the relationship between M and W: 'M = 14W / 4 = 3.5W'. He then calculates the total work using the first scenario: 'Total Work = (4M + 6W) * 5'. He substitutes M with 3.5W: 'Total Work = (4*3.5W + 6W) * 5 = (14W + 6W) * 5 = 20W * 5 = 100W'.

  3. 5:00 – 10:00 05:00-10:00

    The instructor proceeds to find the time for 8 men and 12 women to complete the work. He calculates their combined efficiency: '8M + 12W'. He substitutes M with 3.5W: '8*3.5W + 12W = 28W + 12W = 40W'. He then uses the formula 'Time = Total Work / Combined Efficiency'. He substitutes the values: 'Time = 100W / 40W = 2.5 days'. He then moves to the second problem (Q2) from Wipro NLTH 2019, which states: '6 Men and 8 Boys can do a work in 10 days while 26 Men and 48 Boys can do the same work in 2 days. How many days will it take to complete the work if 15 men and 20 boys work together?'. He writes the first equation: '6M + 8B = 10 days'. He then multiplies this equation by 2.5 to get the work rate of 15 men and 20 boys: '15M + 20B = 10 / 2.5 = 4 days'. He then moves to the third problem (Q3) from GATE ECE 2017, which involves men and women building a bridge. He writes the first scenario: '1200 men and 500 women can build a bridge in 2 weeks'. He then writes the second scenario: '900 men and 250 women can build the bridge in 3 weeks'. He equates the total work: '(1200M + 500W) * 2 = (900M + 250W) * 3'. He expands both sides: '2400M + 1000W = 2700M + 750W'. He simplifies: '1000W - 750W = 2700M - 2400M', which becomes '250W = 300M'. He solves for W: 'W = 300M / 250 = 1.2M'. He then calculates the total work: 'Total Work = (1200M + 500W) * 2'. He substitutes W with 1.2M: 'Total Work = (1200M + 500*1.2M) * 2 = (1200M + 600M) * 2 = 1800M * 2 = 3600M'. He then calculates the time for 1200 men to build the bridge in one week: 'Time = Total Work / (1200M * 1) = 3600M / 1200M = 3 weeks'. He then moves to the final problem (Q4), which states: 'Manmohan Ji, Sonia Gandhi Ji and Kejriwal Ji can complete a piece of work in 24, 6 and 12 days respectively when they work alone. Working together, they will complete the same work in?'. He writes the formula for combined work rate: '1 / (1/24 + 1/6 + 1/12)'. He calculates the sum: '1/24 + 4/24 + 2/24 = 7/24'. He then calculates the time: '24/7 days'.

  4. 10:00 – 10:53 10:00-10:53

    The video concludes with a final problem on the screen. The problem states: 'Manmohan Ji, Sonia Gandhi Ji and Kejriwal Ji can complete a piece of work in 24, 6 and 12 days respectively when they work alone. Working together, they will complete the same work in?'. The instructor writes the formula for combined work rate: '1 / (1/24 + 1/6 + 1/12)'. He calculates the sum: '1/24 + 4/24 + 2/24 = 7/24'. He then calculates the time: '24/7 days'. The video ends with a 'THANKS FOR WATCHING' screen.

The video presents a structured and progressive lesson on solving time and work problems. It begins with a foundational problem that introduces the core concept of equating total work using variables for individual efficiencies. The instructor methodically demonstrates how to set up and solve equations to find the relationship between different work rates. The lesson then transitions to more complex problems, including those with different worker types (men/boys, men/women) and those requiring the calculation of combined work rates. The key methodological takeaway is the consistent application of the formula 'Total Work = Men * Efficiency * Time' and the strategic use of algebra to solve for unknowns. The video effectively uses a digital whiteboard to clearly illustrate each step of the problem-solving process, making it a valuable resource for students preparing for competitive exams.