Time and Work | Efficiency based questions/Problems | Day 3(2020)
14Welcome to this video on time and work efficiency-based problems in mathematics. In this video, we'll be discussing problems related to the amount of work done, the time it takes to complete it, and how the efficiency of the workers affects the overall completion time.
We'll start by going over some basic formulas and concepts that are essential for solving these types of problems. Then, we'll move on to some examples to help you understand how to apply these concepts to real-life scenarios.
Whether you're a student preparing for an exam or just someone looking to improve your problem-solving skills, this video will provide you with a solid foundation in time and work efficiency problems. So, if you want to learn how to calculate the time it takes to complete a task or how much work can be done in a given time period, taking into account the efficiency of the workers, make sure to watch this video until the end.
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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).
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Q1. A is twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B together finish the work is:
a) 4 days b) 6 days c) 8 days d) 18 days
Q2. A is twice as good a workman as B and together they finish a piece of work in 14 days. In how many days A alone can finish the work?
a) 11 days b) 12 days c) 28 days d) 42 days
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