Time and Work | Problems based on Fraction of work | Best Short Tricks(2020)
31In this video, we will dive into the concept of time and work, specifically focusing on problems that involve the fraction of work done by each worker. We will begin by discussing the basic concepts of time and work, and then move on to problems where workers have different levels of efficiency.
We will cover the fraction of work formula and how to apply it to solve problems where workers join or leave the project at different times. We will also discuss how to find the total time taken to complete a project and how to calculate the individual worker's efficiency.
Whether you are a student preparing for an exam or a professional looking to sharpen your math skills, this video is perfect for you. By the end of this video, you will have a thorough understanding of the fraction of work concept and be able to apply it to various time and work problems.
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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. A train 300 meters long is running at a speed of 54 km/hr. In what time will it cross a telephone pole?
(a)18 seconds (b)17 seconds (c)20 seconds (d)15 seconds
Q2. A and B together can do a job in 12 days. B alone can finish it in 28 days. In how many days can A alone finish the work?
a. 21 b. 19 c. 20 d. None
Q3. A and B can do a piece of work in 12 days, B and C in 15 days, C and A in 20 days. In how many days will the job finished, if A, B and C work together?
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