Time and Work | Problems on Chain Rule | Best Short Trick(2020)
16In this video, we will learn about the time and work chain rule, which is a crucial concept in solving problems related to work done by multiple people in a given time. We will start by understanding the basic concepts of time and work, and then move on to the chain rule, which is used when multiple people work together to complete a task.
We will discuss how to apply the chain rule to problems involving both partial and complete work done by each person. We will also cover some common variations of the time and work chain rule, including problems involving efficiency and varying work rates.
By the end of this video, you will have a thorough understanding of the time and work chain rule and how to apply it to various problems. So, whether you are a student preparing for an exam or a professional looking to sharpen your math skills, this video is perfect for you.
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Introduction
In these types of problems, the basic concept of efficiency is involved. All of these kinds of problems can be solved through either unitary method or variations or percentage efficiency.
The same principle of ‘time and work’ is used to solve the problems on ‘Pipes and Cisterns’. The only difference is that in this case, the work done is in terms of filling or emptying a cistern (tank) and the time is by a pipe or a leak (crack) to fill or empty a cistern. The work done by the outlet pipe will be taken as negative.
Important Points
1. If A can do a work in X days.
Then, A’s one day’s work = 1/Xth part of whole work
2. If A’s one day’s work = 1/Xth part of whole work
Then, A can finish the work in X days.
3. If A can do a piece of work in X days and B can do it in Y days. When A and B working together
A’s + B’s one day’s work = X+Y/XY
Or Days needed = XY/X+Y
4. If A, B, C ... can do a work in X, Y, Z, ... days respectively. Then if all of them working together
Team’s one’s day work = 1/x +1/y + ....
Days needed = 1/one day work
5. If A and B together can do a piece of work in X days and A alone can do it in Y days.
Then, days need by B alone = XY/Y-X
6. A and B can do a work in X and Y days respectively. They started the work together but A left ‘a’ days before completion of the work.
Then, days needed = Y(X+a)/X+Y
7. If A is n times as efficient as B, i.e. A has n times as much capacity to do work as B, A will take 1/nth of the time as compared to B.
8. If A is a times as efficient as B and A can finish a work in X days.
Then, days needed to do the work togather = ax/a+1
9. If A is a times as efficient as B and working together they finish a work in Z days.
Then, days taken by A alone = Z(a+1)/a
and days taken by B alone = Z (a + 1)
10. A is a times efficient than B and takes X days less than B to finish the work.
Then, days taken by both = ax/a2-1
11. If A working alone takes ‘x’ days more than A and B together and B working along takes ‘y’ days more than A and B together.
Then, days required working together = /xy
12. If M men do a work (W) in D days by working for T hours per day with E efficiency, then
M1D1W2T1E1 = M2D2W1T2E2
13. Wages are distributed in proportion to the work done and in reverse (indirect) proportion to the time taken by the individual.
14. The time required by a pipe to fill or empty a cistern is proportional to the square of its diameter
(or radius).
Q1. If 120 men can do a job in 100 days, in how many days will 150 men do it.
Q2. If 18 men working 5 hours a day for 8 days can complete a job, how many men working 8 hours a day for 6 days will be needed?
Q3. If 4 men reap 40 acres in 30 days, how many acres will 18 men reap in 12 days?
Q4. If 12 men can build a wall 100 meter long, 3m high and 0.5 m thick in 25 days, in how many days will 20 men build a wall 60m long, 4m high and 0.25 m thick.
Q5. 15 men take 21 days of 8 hours each to do a work. How many days of 6 hours each would 21 women take, if 3 women do as much work as 2 men?
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