In most of the problems based on Time and Work, either the amount of time taken to finish a given job or the amount of work done is to be calculated. Unless otherwise specified, the amount of work done is generally taken as unity (1). Also if it is given that a person (P) can finish a job in D days, then it implies that P alone can do the job in D days.
Important Points to Remember :
(i) Capacity of persons to do a piece of work is always constant. That is, the person does the equal work every day.
(ii) In the question based on ‘Time and Work’, generally we find amount of work done in unit time (1 day, 1 hour etc). Thus, if a man can do a piece of work in x days (or hours or any other unit of time), then the work done by him in one day will be(1\x) of the total work
(iii) If A is twice as good as a workman as B, then A will take half the time B takes to finish a piece of work.
(iv) Application of the Concept of Unitary Method and Variation: Since in problems on Time and Work, there is a proportional relation, hence we solve them by Unitary Method and Ratio and Proportion
(v) If to finish a certain piece of work, some men are employed and they finish the work in a certain time, then the relation between work, man and time will be as follows:
(a) Work and Man: Number of persons employed to do the work is directly proportional to the amount of work done. (More t he number of personsemployed, more the work done)
(b) Time and Work: The number of days is directly proportional to work done. (More the number of days for which a work was done, more shall be the total amount of work done)
(c) Time and Man: The number of persons employed is inversely proportional to the number of days required to finish a work. (More the number of persons employed, less will be the time required to finish the work)
1: Amit can do a piece of work in 4 days and Sumit can do it in 6 days. How long will they take, if both Amit and Sumit work together?
We have, time taken by Amit to do the work = 4 days
Time taken by Sumit to do the work = 6 day
Work done by Amit in 1 day = 1/4
Work done by Sumit in 1 day = 1\6
So, work done by Amit and Sumit in 1 day
Hence, Amit and Sumit can do the piece of work in 12\5 days i.e 2(5/12)