Time and Work:
- Work to be done is generally considered as one unit. It may be digging a trench constructing or painting a wall, filling up or emptying a tank, reservoir or a cistern.
General rules to be followed in the problems on Time and Work
1. If A can do a piece of work in n days, then work done by A in 1 day is I/n. ie,if a person can do some work in 12 days, he does 1/ 12th of the work in one day.
2. If A’s 1 day’s work = 1/n, then A can finish the whole work in n days. ie, if a person’s one day work is 1/10, then he can finish the whole work in 10 days.
3. If A is thrice as good a workman as B, then ratio of work done by A and B = 3 : 1. ie, if a man works three times as fast as a woman does, then when the work is complete, 3 parts of the work has been done by the man and 1 part by the woman.
4. If A is thrice as good a workman as B, then ratio of time taken by A and B = 1 : 3. ie, if the woman takes 15 days to complete the work, then the man takes 5 days to complete the same work.
5. If two persons A and B can individually do some work in a and b days respectively, then A and B together can complete the same work in ab (a + b) days.
6. The fundamental rules on variation also apply in Time and Work.
(i) Work and men are directly proportional to each other ie, if the work increases, the no. of men required to do it, also increases, if the work is to be completed in the same number of days.
(ii) Men and days are inversely proportional, ie, if the number of men increases, the number of days required to complete the same work decreases and vice versa.
(iii) Work and days are directly proportional, ie, if the work increases, the number of days required also increases, if the work is to be completed with the same number of men and vice versa.