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Basic Concepts in time and work

                         Time and Work

Time and Work is a another important concepts in aptitude. Pipes and cistern is an application of time and work.
  • Time and Work is directly proportional , where if work increases, time also increases.
  • Work and person is directly proportional, where if  work increases , persons also increases.
  • Time and Person is inversely proportional , where if person increases ,time decreases.

Formulas :

  • If `A` completes work in `n` days , then the work completed in one day is 1/n th part of work.
  • If `A` completes 1/n th work in one day, then total work completed in `n` days.
  • Let us assume `A` completes the work in `n` days and `B` completes the work in `m` days .Let us take work as only one unit, the amount of work done in one day by `A` is 1/n similarly for `B` is 1/m. So in how many days the work is completed if they work together then ,A + B = 1/n + 1/m.


Problems : 

1. If `A` completes the work in 20 days and `B` completes the work same work in 30 days. In how many days both `A` and `B` completes the same work?

Ans :
        Let us assume some units of work , so let us take LCM of both days that will be the total units of work.
        Total units of work = 60 units.
        `A` Completes the no of units work in One day = 60 / 20 = 3.
        `B` Completes the no of units work in One day = 60 / 30 = 2.
        No of days will take by both of persons is  
                =  60 / No of units completed in one day by `A` +  No of units completed in one day by `B` 
                =  60 / 3+2
                = 12
That is 12 days.
                    


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