In this lesson we will discuss one of the most easiest and important topic i.e. WORK.
DEFINITION
|
Technically speaking, Work is the quantity of energy
transferred from one system to another but for question based
on this topic- Work is defined as the amount of job assigned or the amount of job actually done. Problem on work are based on the application of concept of ratio of time and speed. |
Work is always considered as a whole or one.
There exists an analogy between the time-speed-distance problems
and work.
Work based problem are more or less related to time speed and
distance.
Above mentioned definition of work throws light on three
important points.
- Work = 1 ( as it is always measured as a whole) = Distance
- Rate at which work is done = speed
- Number of days required to do the work = Time
IMPORTANT FORMULAE
FOR WORK RELATED PROBLEMS
-
If A can do a piece of work in 'a' number of
days, then in 1 day
of the work is done. Conversely, if a man does
days.
Example: If a man can complete a work in 10 days.How much work he can do in 6 days?
Solution:
= A man will perform in 1 day =
A man performs in 10 days = 1 work.work
-
If A is 'x' times as good a workman as B, then he will take
of the time by B to do the same work.
Example: If A can complete a work in 10 days and B is 100 faster than A. How much time B will take to complete the work?
Solution:
A takes to perform 1 work = 10 days.
= B will perform the same work =time than A.
= B will take to perform the same work =
-
If A and B can do a piece of work in 'a' days and 'b' days respectively, then working together, they will take
days to finish the work and in one day, they will finish
part of work.
Example: If A can do a piece of work in 10 days and B needs 20 days to perform the same work, find out:
- How much time will it take if both work together?
- How much of work they will complete in a day?
Solution:
Number of days to complete the work =
days = 6.66 = 7 days approx
Work complete in one day =
=
-
To compare the work done by two or more people, you first need to calculate the amount of work each can do in the same time.
-
If the number of men to do a job is changed in the ratio a : b, then the time required to do the work will be changed in the inverse ration, i.e. b : a.
Note: Assumed that the work done by any of them is equal and identical.
Example: If 10 men are working on a project and can complete the work in 10 days. 5 of them are placed at some other work, then how much time will take remaining to perform the job?
Solution:
Men at work earlier = 10
Men at work later = 5
Ration of workers = a : b = 2 : 1
10 men can perform the complete task = 10 days
5 men will perform the same task in = b : a time = 1 : 2 => 20 days.<BR?
-
If two man A and B together can finish a job in 'x' days and if A alone takes 'a' days more than A and B working together and B working alone takes 'b' days more than A and B working together then
Example: If A alone can perform a work in 5 days more than A and B working together and B working alone can complete the same work in 20 days more than A and B working together then find out how much time it will take A and B both working together?
Solution:
a = 5; b = 20
=
-
To do a piece of work, the number of men employed and the number of days required to do the work are in inverse proportion.
If it takes 1 men to do a work in 2 days it will always 1 day if the task is performed by 2 men.
SOME SOLVED EXAMPLES
Example 1:
A group of men completes a work in 10 days, but five of them are absent and so the rest do the work in 12 days. Find the original number of Men.
Solution:
More men, less days.
= Total men at work =
30Example 2:
IF 3 men or 5 women take 26 days to do a work, how long will 7 men and 10 women take?
Solution:10 women = 6 men and more men = lesser days.
Example 3:
If 30 men working 7 hours per day can do a work
in 18 days in how many days will 21 men working 8 hours a day do
the same work?
Solution:
Fewer men, more day; more hours; fewer days.
>br>
Number of days = 22.5
Post Comments