Time and work
While solving problems on time and work, unitary method is used i.e. value of a unit quantity is first obtained to find the value of any required quantity. Remember the following things when solve problems on them. The time required to complete a work depends upon the number of persons employed.
1. if number of hours ( or days) to complete a work is given, then work in one hour ( or one day)
1
= ____________
Number of hours (or days)
E.g. a can do a piece of work in 5 hours
1
There fore, in one hour, he does ___ of the
5
If the work in one hour is given, then the time taken to complete the whole work
1
= _____________________________
It is One hour’s (or one day’s) work.
1
E.g. B does _____ of a work in one day.
4
1
Therefore, he completes the whole work in ______ = 4 days.
1/ 4
Definition of variation-: The change in two different variables is following some definite rule. It is said that
X
The two variables vary directly or inversely. Its notation is __ = K, where K, is called the constant. This
Y
Variation is called inverse variation.
X Y = k, this variation is called inverse variation.
Some pairs of variables
1) Number of workers and their wages. If the number of workers increases, their total wages increase. If the number of days is reduced, there will be less work. If the number of days is increased, there will be more work; therefore, here we have direct proportion or direct variation.
2) Number of workers and days required to do a certain work in example of inverse variation. If more men or employed, they will require few days and if there are less number of workers, more days are required.
3) There is inverse proportion between the daily hours of work and the days required. If the number of hours is increased, less number of days is required and if the number of hours is reduced, more days are required.
Important tips
More men- less days and conversely more days- less men.
More men- more work and conversely more work-more men
More days- more work and conversely more work- more days
Number of days required to complete the given work:-
Total work
= ___________
One day’s work
Since the total work is assumed to be one 9unit), the number of days required to complete the given work would be the reciprocal of one day’s work. Some times, the problem on time and work can be solved using proportional rule.
1
(Man x days x hour x _____.) In another situation.
Work
Example
`A ‘can do a piece of work in 5 days and `B’ in 4 days. How long will they take to do the same work working together?
Solution:-
A does the work in 5 days. B does the work in 4 days.
Amount of work done by an in one day = 1/ 5
A mount of work dine by B in one day = 1/ 4
A mount of work done by A & B in one day = 1/ 5 + 1/ 4 = 9/ 20
2
Number of days required to complete the work = 20/ 9 = 2 ____ days.
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