Work is defined as the amount of job assigned or the amount of job actually done.
2. Important Formulae
2.1. Work from Days
If A can do a piece of work in n days, then A's 1 day's work =1/n
If A's 1 day's work =1/n
, then A can finish the work in n days.
1. If A is thrice as good a workman as B, then:
(i) Ratio of work done by A and B =3:1.
(ii) Ratio of times taken by A and B to finish a work =1:3
(iii) If A is x times as good a workman as B, then he will take (1/x)th
of the time by B to do the same work.
Some important conclusions:
1. A and B can do a piece of work in 'x' days and 'y' days respectively, then working together, they will take = ”xy/x+y” days.
in one day both will finish (x+y/xy)th part of work.
2. If A , B and C separately can do a work in x , y and z days respectively, the number of days required by them to complete the whole work are= xyz/(xy+yz+zx) days.
3. If A and B together can do a work in ‘x’ days and one of them completes the same amount of work in ‘y’ days. Then another one will take = xy/y-x days to complete the same work.
4. If x1 persons , working t1 hours everyday, finishes w1 amount of work in n1 days. While x2 persons , working t2 hours everyday, finishes w2 amount of work in n2 days then
“x1t1n1w2 = x2t2n2w1”.
5. If “A” number of persons can complete a work in “D” days, if there was “a” number of less persons than it would take “d” more days to finish the work.
Then Ad = a(D+d).