TLDR;
This video introduces the concept of time and work problems and provides a formula (MDH/W) to solve them. It explains the components of the formula (men, days, hours, work) and demonstrates its application through several examples, gradually increasing in complexity. The video covers problems involving finding the number of days, hours, or wages based on given data.
- Introduces the MDH formula for solving time and work problems.
- Explains each component of the formula with examples.
- Solves five different types of problems, increasing in difficulty.
Introduction to Time and Work [0:00]
The video starts with an introduction to time and work problems, explaining that it will cover various types of questions solvable using the MDH formula. The approach will be step-by-step, moving from simple to complex problems to ensure easy understanding. The core formula introduced is M1D1H1/W1 = M2D2H2/W2, where M stands for men/women, D for days, H for hours, and W for work done.
Understanding the MDH Formula [0:30]
The MDH formula is explained in detail, clarifying that M represents the number of men or women working, D represents the number of days, and H represents the number of hours worked per day. W represents the amount of work done, such as making a road or digging a pond. The formula equates the ratios of work done by two different sets of workers, allowing for the calculation of unknown variables.
Problem 1: Finding the Number of Days [1:51]
The first problem involves finding the number of days required for 16 people to complete a task that 12 people can do in 8 days. Using the formula M1D1 = M2D2, the calculation is set up as 12 * 8 = 16 * D2. Solving for D2, the number of days is found to be 6.
Problem 2: Building a Dam [3:34]
In the second problem, 12 men can build a dam in 10 days by working 8 hours a day. The question asks how many days it will take for 12 men to build the same dam working 10 hours a day. The formula M1D1H1 = M2D2H2 is used, and the equation becomes 12 * 10 * 8 = 12 * D2 * 10. Solving for D2, it is determined that it will take 8 days.
Problem 3: Digging a Pond [5:17]
The third problem involves 20 people digging a pond in 12 days by working 7 hours a day. The question asks how many hours per day 24 people must work to dig a pond twice as big in 14 days. The formula M1D1H1/W1 = M2D2H2/W2 is applied, with W1 = 1 and W2 = 2. The equation is set up as (20 * 12 * 7) / 1 = (24 * 14 * H2) / 2. Solving for H2, it is found that they need to work 10 hours per day.
Problem 4: Building a Road [8:33]
The fourth problem states that 24 laborers can build a road in 15 days by working 8 hours a day. The question asks how many days it will take 48 laborers to build a road three times as long by working 6 hours per day. Using the formula M1D1H1/W1 = M2D2H2/W2, with W1 = 1 and W2 = 3, the equation becomes (24 * 15 * 8) / 1 = (48 * D2 * 6) / 3. Solving for D2, it is calculated that it will take 30 days.
Problem 5: Earning Money [10:32]
The fifth problem involves 12 people earning ₹480 by working 8 hours per day. The question asks how much money 18 people will earn by working 12 hours per day. The formula M1H1/W1 = M2H2/W2 is used, where W represents the earnings. The equation is set up as (12 * 8) / 480 = (18 * 12) / W2. Solving for W2, it is found that they will earn ₹1080.
Conclusion [12:08]
The video concludes by emphasizing the importance of understanding and preparing the MDH formula to solve time and work problems effectively. It encourages viewers to like and share the video if they found it helpful.