### Time and Work

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1. Work:

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

2.2

If A's 1 day's work =1/n

, then A can finish the work in n days.

2.3. Ratio

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.

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